Skill: Determine the dimensions of a matrix product

To determine the dimensions of a matrix product, compare the inner dimensions. The product is defined only if they match. If they do, the outer dimensions give the size of the result.

For example, suppose $A$ is a $3 \times 4$ matrix and $B$ is a $4 \times 2$ matrix. In the product $AB$:

1. Write the dimensions in order: $(3 \times 4)(4 \times 2)$.
2. Check the inner dimensions: $4$ and $4$ match, so the product is defined.
3. Read the outer dimensions: $3$ and $2$.

Therefore, $AB$ has dimensions $3 \times 2$. The entries of the matrices do not affect this dimension check.