Calculators / Linear Algebra / Matrix Subtraction Calculator

Matrix Subtraction Calculator

Published on: September 14 2025

This Matrix Subtraction Calculator helps you subtract one matrix from another and shows each step clearly. It works by subtracting the corresponding entries of two matrices with the same dimensions to form a new matrix. This makes it useful for checking answers, understanding how matrix subtraction works, and practising linear algebra step by step.

Step-by-step method

  1. Make sure both matrices have the same dimensions.
  2. Subtract corresponding entries (same position) to form the result matrix.

Formula:

If A = [aij] and B = [bij], then A − B = [aij − bij].

Example 1: 2×2 matrices

Step 1 - Make sure both matrices have the same dimensions.

In this problem: Both matrices are 2×2, so they can be subtracted.

12
-3
40
7
−
5
18
-9
2

Step 2 - Subtract corresponding entries (same position) to form the result matrix.

In this problem: Subtract entries in the same position to form the result matrix.

12−5
-3−18
40−-9
7−2
=
7
-21
49
5

Final answer:

7
-21
49
5

Example 2: 3×3 matrices

Step 1 - Make sure both matrices have the same dimensions.

In this problem: Both matrices are 3×3, so they can be subtracted.

1000
-2
33
4
15
6
7
8
9
−
1
2
30
4
5
6
-7
0
11

Step 2 - Subtract corresponding entries (same position) to form the result matrix.

In this problem: Subtract entries in the same position to form the result matrix.

1000−1
-2−2
33−30
4−4
15−5
6−6
7−-7
8−0
9−11
=
999
-4
3
0
10
0
14
8
-2

Final answer:

999
-4
3
0
10
0
14
8
-2
Matrix A
−
Matrix B