Matrix Multiplication Calculator
This Matrix Multiplication Calculator helps you multiply two matrices and shows each step clearly. In Algebra 2, matrix multiplication is used when working with matrices, systems, transformations, and organized numerical data. It works by taking a row from the first matrix and a column from the second matrix, multiplying corresponding entries, and adding the results to form each entry of the product matrix.
Step-by-step method
- Make sure the number of columns in Matrix A equals the number of rows in Matrix B.
- Multiply each row of Matrix A by each column of Matrix B.
- Add the products to form each entry of the result matrix.
Formula
Example 1: 2×2 matrix times 2×2 matrix
Step 1 - Make sure the number of columns in Matrix A equals the number of rows in Matrix B.
In this problem: Matrix A is 2×2 and Matrix B is 2×2. Since 2 = 2, multiplication is possible.
1 | 2 |
3 | 4 |
5 | 6 |
7 | 8 |
Step 2 - Multiply each row of Matrix A by each column of Matrix B.
In this problem: For each entry, multiply a row of A by a column of B.
1×5 + 2×7 | 1×6 + 2×8 |
3×5 + 4×7 | 3×6 + 4×8 |
Step 3 - Add the products to form each entry of the result matrix.
In this problem: Add each row-column product to get the final matrix.
19 | 22 |
43 | 50 |
Final answer:
19 | 22 |
43 | 50 |
Example 2: 2×3 matrix times 3×2 matrix
Step 1 - Make sure the number of columns in Matrix A equals the number of rows in Matrix B.
In this problem: Matrix A is 2×3 and Matrix B is 3×2. Since 3 = 3, multiplication is possible.
2 | -1 | 3 |
0 | 4 | 5 |
1 | 2 |
3 | 0 |
-2 | 1 |
Step 2 - Multiply each row of Matrix A by each column of Matrix B.
In this problem: For each entry, multiply a row of A by a column of B.
2×1 + -1×3 + 3×(-2) | 2×2 + -1×0 + 3×1 |
0×1 + 4×3 + 5×(-2) | 0×2 + 4×0 + 5×1 |
Step 3 - Add the products to form each entry of the result matrix.
In this problem: Add each row-column product to get the final matrix.
-7 | 7 |
2 | 5 |
Final answer:
-7 | 7 |
2 | 5 |