Matrix Multiplication Calculator
This Matrix Multiplication Calculator helps you multiply two matrices and shows each step clearly. It works by taking the row of the first matrix and the column of the second matrix, multiplying corresponding entries, and then adding the results to form each entry of the product matrix. This makes it useful for checking answers, understanding how matrix multiplication works, and practising linear algebra step by step.
Step-by-step method
- Check the dimensions (Cols A must equal Rows B).
- Multiply row-by-column to get each entry.
Formula
Example 1: A (2×2) × B (2×2)
Step 1 - Check the dimensions (Cols A must equal Rows B).
In this problem: A is 2×2 and B is 2×2, so A × B is defined and will be 2×2.
1 | 2 |
3 | 4 |
5 | 6 |
7 | 8 |
Step 2 - Multiply row-by-column to get each entry.
In this problem: Each entry is a dot product of a row of A with a column of B.
1×5 + 2×7 | 1×6 + 2×8 |
3×5 + 4×7 | 3×6 + 4×8 |
19 | 22 |
43 | 50 |
Final answer:
19 | 22 |
43 | 50 |
Example 2: A (2×3) × B (3×2)
Step 1 - Check the dimensions (Cols A must equal Rows B).
In this problem: A is 2×3 and B is 3×2, so A × B is defined and will be 2×2.
2 | 0 | -1 |
3 | 1 | 4 |
1 | 2 |
0 | 5 |
-2 | 3 |
Step 2 - Multiply row-by-column to get each entry.
In this problem: Each entry is a dot product of a row of A with a column of B.
2×1 + 0×0 + (-1)×(-2) | 2×2 + 0×5 + (-1)×3 |
3×1 + 1×0 + 4×(-2) | 3×2 + 1×5 + 4×3 |
4 | 1 |
-5 | 23 |
Final answer:
4 | 1 |
-5 | 23 |
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