Question

For which condition does the product \[AB\] exist?

Options

• Columns of \[A\] = columns of \[B\]

• Columns of \[A\] = rows of \[B\]

• Rows of \[A\] = columns of \[B\]

• Rows of \[A\] = rows of \[B\]

Answer 1

The product \[AB\] exists only when the columns of \[A\] equal the rows of \[B\]. This matching condition allows each row of \[A\] to multiply a column of \[B\].