Question

When can we multiply matrices?

A) When they have the same dimensions.
B) When the matrices are squared matrices.
C) When the inner dimensions are the same.
D) When the outer dimensions are the same.

Answer 1

Matrices can be multiplied when the number of columns in the first matrix matches the number of rows in the second matrix, also known as when the inner dimensions are the same.

Step-by-step explanation:

We can multiply matrices when the inner dimensions are the same, meaning the number of columns in the first matrix must match the number of rows in the second matrix.

It is not necessary for the matrices to have the same overall dimensions, to be square matrices, or for the outer dimensions to be the same.

For example, if we have two matrices, A and B, with dimensions of 2x3 and 3x2 respectively, we can multiply them because the inner dimension 3 (columns of A and rows of B) is the same.

The result of this multiplication will be a new matrix with the outer dimensions, which in this case is 2x2.