Question

If $A=\left[\begin{array}{ccc}1& -2& 1\\ 2& 1& 3\end{array}\right]$ and $B=\left[\begin{array}{cc}2& 1\\ 3& 2\\ 1& 1\end{array}\right]$, then ${\left(AB\right)}^T$ is equal to

• A. $\left[\begin{array}{cc}-3& -2\\ 10& 7\end{array}\right]$
• B. $\left[\begin{array}{cc}-3& 10\\ -2& 7\end{array}\right]$
• C. $\left[\begin{array}{cc}-3& 7\\ 10& 2\end{array}\right]$
• D. None of these

Answer 1

Answer: (B)

$\left[\begin{array}{cc}-3& 10\\ -2& 7\end{array}\right]$

Given, $A=\left[\begin{array}{ccc}1& -2& 1\\ 2& 1& 3\end{array}\right],B=\left[\begin{array}{cc}2& 1\\ 3& 2\\ 1& 1\end{array}\right]$
$\therefore AB=\left[\begin{array}{cc}2-6+1& 1-4+1\\ 4+3+3& 2+2+3\end{array}\right]=\left[\begin{array}{cc}-3& -2\\ 10& 7\end{array}\right]$
Now, ${\left(AB\right)}^T=\left[\begin{array}{cc}-3& 10\\ -2& 7\end{array}\right]$