Question

If A=$\left[\begin{array}{ccc}1& 2& 3\\ 2& -3& 0\end{array}\right]$ and B=$\left[\begin{array}{ccc}3& 4& -2\\ 1& 0& 0\end{array}\right]$ then the order of $A{B}^T$ is _______

• A. $2\times 3$
• B. $3\times 3$
• C. $3\times 2$
• D. $2\times 2$

Answer 1

The correct option is D $2\times 2$

As B is of order $2\times 3$, then $B^T$ will have the order $3\times 2$,
When a matrix of order $m\times a$ is multiplied with a matrix of order $a\times n$, the resulting matrix is of order $m\times n$
As A is of order $2\times 3$ and $B^T$ has the order $3\times 2$, we get $a=3;m=2;n=2$
So, product matrix $A{B}^T$ will have the order $2\times 2$