Matrix size tool
Choose the rows and columns of Matrix A and Matrix B to check whether A × B is defined, what size the result will be, and whether B × A is also possible.
Current size: 2 × 3
Current size: 3 × 2
A × B is possible
Matrix A: 2 × 3
Matrix B: 3 × 2
Inner dimensions 3 = 3
Result dimensions 2 × 2
The inner dimensions match, so A × B is defined. The result keeps the rows of A and the columns of B.
To make A × B possible:
B × A is also possible
Inner dimensions 2 = 2
Result dimensions 3 × 3
The reverse order is defined for these dimensions, but it may produce a different result size.
For A × B, compare the number of columns in A with the number of rows in B. The product is defined only when those two numbers match.
When A is m × n and B is n × p, the result keeps the rows of A and the columns of B, so A × B is m × p.
Yes. A × B being possible does not mean B × A is possible. Even when both products are defined, their result dimensions can be different, and matrix multiplication is usually not commutative.
The columns of the first matrix must match the rows of the second matrix because each result entry is built from one row and one column with the same number of terms.
If A is m by n and B is n by p, then A × B is defined and the result size is m by p.
Yes. A × B depends on the columns of A and rows of B, while B × A depends on the columns of B and rows of A.
Yes. Matrix multiplication order usually matters. Even when both A × B and B × A exist, their result sizes or values can be different.
This checker tests row and column counts from 1 to 9, matching the current matrix calculator size controls.