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Matrix Multiplication in Java – Complete Java Program with Explanation (Part 2A)

Introduction

In Part 1, we learned:

  • What a matrix is
  • Conditions for matrix multiplication
  • The Row × Column rule
  • How to perform matrix multiplication manually

Now it’s time to convert that knowledge into a Java program.

By the end of this tutorial, you will be able to:

  • Accept two matrices from the user.
  • Check whether multiplication is possible.
  • Multiply the matrices.
  • Display the result matrix.
  • Understand the purpose of every loop in the program.

Algorithm for Matrix Multiplication

Before writing the code, let’s understand the algorithm.

Step 1

Read the dimensions of the first matrix.

firstMatrixRows
firstMatrixColumns

Step 2

Read the dimensions of the second matrix.

secondMatrixRows
secondMatrixColumns

Step 3

Check whether multiplication is possible.

If firstMatrixColumns != secondMatrixRows

    Display "Multiplication Not Possible"

Else

    Continue

Step 4

Create three matrices.

First Matrix

Second Matrix

Result Matrix

Step 5

Read all elements of the first matrix.

Step 6

Read all elements of the second matrix.

Step 7

Multiply the matrices.

Step 8

Display the result matrix.

Understanding the Three Nested Loops

This is the heart of the program.

We already know that

(m × n)

×

(n × p)

=

(m × p)

The three loops represent:

for(row)

Moves through

Rows of First Matrix

for(column)

Moves through

Columns of Second Matrix

for(common)

Moves through

Columns of First Matrix

=

Rows of Second Matrix

Remember this forever.

Row

↓

Column

↓

Common Dimension

Complete Java Program

import java.util.Scanner;

public class MatrixMultiplication {

    public static void main(String[] args) {

        Scanner sc = new Scanner(System.in);

        // Input dimensions of first matrix
        System.out.print("Enter number of rows of First Matrix: ");
        int firstMatrixRows = sc.nextInt();

        System.out.print("Enter number of columns of First Matrix: ");
        int firstMatrixColumns = sc.nextInt();

        // Input dimensions of second matrix
        System.out.print("Enter number of rows of Second Matrix: ");
        int secondMatrixRows = sc.nextInt();

        System.out.print("Enter number of columns of Second Matrix: ");
        int secondMatrixColumns = sc.nextInt();

        // Check whether multiplication is possible
        if (firstMatrixColumns != secondMatrixRows) {

            System.out.println("\nMatrix multiplication is NOT possible.");

            System.out.println(
                    "Columns of First Matrix must be equal to Rows of Second Matrix.");

            sc.close();
            return;
        }

        // Create matrices
        int firstMatrix[][] =
                new int[firstMatrixRows][firstMatrixColumns];

        int secondMatrix[][] =
                new int[secondMatrixRows][secondMatrixColumns];

        int resultMatrix[][] =
                new int[firstMatrixRows][secondMatrixColumns];

        // Input first matrix
        System.out.println("\nEnter elements of First Matrix:");

        for (int row = 0; row < firstMatrixRows; row++) {

            for (int column = 0; column < firstMatrixColumns; column++) {

                firstMatrix[row][column] = sc.nextInt();
            }
        }

        // Input second matrix
        System.out.println("\nEnter elements of Second Matrix:");

        for (int row = 0; row < secondMatrixRows; row++) {

            for (int column = 0; column < secondMatrixColumns; column++) {

                secondMatrix[row][column] = sc.nextInt();
            }
        }

        // Matrix Multiplication
        for (int row = 0; row < firstMatrixRows; row++) {

            for (int column = 0; column < secondMatrixColumns; column++) {

                for (int common = 0;
                     common < firstMatrixColumns;
                     common++) {

                    resultMatrix[row][column] +=
                            firstMatrix[row][common] *
                            secondMatrix[common][column];
                }
            }
        }

        // Display Result Matrix
        System.out.println("\nResult Matrix:");

        for (int row = 0; row < firstMatrixRows; row++) {

            for (int column = 0; column < secondMatrixColumns; column++) {

                System.out.print(resultMatrix[row][column] + "\t");
            }

            System.out.println();
        }

        sc.close();
    }
}

Understanding the Program Step by Step

Let’s understand every important section of the program.

Step 1: Reading Matrix Dimensions

System.out.print("Enter number of rows of First Matrix: ");
int firstMatrixRows = sc.nextInt();

System.out.print("Enter number of columns of First Matrix: ");
int firstMatrixColumns = sc.nextInt();

Here, we ask the user to enter the size of the first matrix.

For example,

Rows = 2

Columns = 3

This means the first matrix will contain

2 Rows

3 Columns

Similarly,

System.out.print("Enter number of rows of Second Matrix: ");
int secondMatrixRows = sc.nextInt();

System.out.print("Enter number of columns of Second Matrix: ");
int secondMatrixColumns = sc.nextInt();

Suppose the user enters

Rows = 3

Columns = 2

Step 2: Checking Whether Multiplication is Possible

This is the most important validation.

if (firstMatrixColumns != secondMatrixRows) {

    System.out.println("Matrix multiplication is NOT possible.");

    return;
}

Suppose the user enters

First Matrix

2 × 3

Second Matrix

4 × 2

Compare

First Matrix Columns = 3

Second Matrix Rows = 4

Since

3 ≠ 4

Multiplication cannot be performed.

The program immediately stops.

This prevents invalid calculations and runtime errors.

Step 3: Creating the Matrices

int firstMatrix[][] =
new int[firstMatrixRows][firstMatrixColumns];

Creates the first matrix.

Similarly,

int secondMatrix[][] =
new int[secondMatrixRows][secondMatrixColumns];

creates the second matrix.

Finally,

int resultMatrix[][] =
new int[firstMatrixRows][secondMatrixColumns];

creates the result matrix.

Notice carefully.

The result matrix uses

Rows of First Matrix

Columns of Second Matrix

Exactly as we learned in Part 1.

Step 4: Reading Matrix Elements

for(int row=0; row<firstMatrixRows; row++)
{
    for(int column=0;
        column<firstMatrixColumns;
        column++)
    {
        firstMatrix[row][column]=sc.nextInt();
    }
}

The outer loop moves through every row.

The inner loop moves through every column.

Together they read every element of the matrix.

Exactly the same logic is used for the second matrix.

Step 5: Matrix Multiplication

This is the most important part of the program.

for(int row=0; row<firstMatrixRows; row++)
{
    for(int column=0;
        column<secondMatrixColumns;
        column++)
    {
        for(int common=0;
            common<firstMatrixColumns;
            common++)
        {
            resultMatrix[row][column]+=

                firstMatrix[row][common]

                *

                secondMatrix[common][column];
        }
    }
}

Remember the meaning of every variable.

row

↓

Current Row of First Matrix

column

↓

Current Column of Second Matrix

common

↓

Common Dimension

Columns of First Matrix

Rows of Second Matrix

This exactly follows the Row × Column rule.

Why is the Inner Loop Named “common”?

Many books use

k

Instead of

common

However,

common

is much easier to understand.

It represents the

Common Dimension

Columns of First Matrix

=

Rows of Second Matrix

For every value of

common

the program multiplies one element from the selected row of the first matrix with the corresponding element from the selected column of the second matrix.

Sample Input

Enter number of rows of First Matrix:
2

Enter number of columns of First Matrix:
3

Enter number of rows of Second Matrix:
3

Enter number of columns of Second Matrix:
2

Enter elements of First Matrix

1 2 3

4 5 6

Enter elements of Second Matrix

7 8

9 10

11 12

Output

Result Matrix

58    64

139   154

Key Takeaways

  • Always check whether multiplication is possible before performing any calculations.
  • Matrix multiplication is possible only when the columns of the first matrix equal the rows of the second matrix.
  • The result matrix size is Rows of First Matrix × Columns of Second Matrix.
  • The program uses three nested loops:
    • The first loop selects each row of the first matrix.
    • The second loop selects each column of the second matrix.
    • The third loop traverses the common dimension and computes the dot product.
  • Using descriptive variable names like row, column, and common makes the algorithm much easier to understand than using generic variables such as i, j, and k.

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