Question

If \[A\] is \[m \times n\] and \[B\] is \[n \times p\], what is the order of \[AB\]?

Options

• \[n \times p\]

• \[n \times m\]

• \[m \times n\]

• \[m \times p\]

Answer 1

For \[A\] of order \[m \times n\] and \[B\] of order \[n \times p\], the inner dimensions \[n\] match. The product \[AB\] therefore has the outer dimensions \[m \times p\].