Question

If A = $\left[\begin{array}{cc}1& 5\\ 6& 2\end{array}\right]$ and B = $\left[\begin{array}{cc}3& 7\\ 8& 4\end{array}\right]$, then $A{B}^T$ is equal to

• A. $$\left[\begin{array}{cc}38& 28\\ 32& 56\end{array}\right]$$
• B. $$\left[\begin{array}{cc}3& 40\\ 42& 8\end{array}\right]$$
• C. $$\left[\begin{array}{cc}43& 27\\ 34& 50\end{array}\right]$$
• D. $$\left[\begin{array}{cc}38& 32\\ 28& 56\end{array}\right]$$

Answer 1

The correct option is A $$\left[\begin{array}{cc}38& 28\\ 32& 56\end{array}\right]$$

$A=\left[\begin{array}{cc}1& 5\\ 6& 2\end{array}\right]$
$B=\left[\begin{array}{cc}3& 7\\ 8& 4\end{array}\right]$
$A{B}^T=\left[\begin{array}{cc}1& 5\\ 6& 2\end{array}\right]\left[\begin{array}{cc}3& 8\\ 7& 4\end{array}\right]$
$=\left[\begin{array}{cc}3+35& 8+20\\ 18+14& 48+8\end{array}\right]$
$=\left[\begin{array}{cc}38& 28\\ 32& 56\end{array}\right]$