Question

If $A=\begin{bmatrix} {3}&{5}\\\ {2}&{0}\\\ \end{bmatrix}$ and $B$ = $\begin{bmatrix} {1}&{17}\\\ {0}&{-10}\\\ \end{bmatrix}$then $|AB|$ is equal to

• A. 80
• B. 100
• C. -110
• D. 92

Answer 1

Answer: (B)

100

Answer 2

$A=\begin{bmatrix}3 & 5 \\\ 2 & 0\end{bmatrix}$ and $B=\begin{bmatrix}1 & 17 \\\ 0 & -10\end{bmatrix}$ $\therefore \, A B=\begin{bmatrix}3 & 5 \\\ 2 & 0\end{bmatrix}\begin{bmatrix}1 & 17 \\\ 0 & -10\end{bmatrix}$ $=\begin{bmatrix}3+0 & 51-50 \\\ 2+0 & 34-0\end{bmatrix}=\begin{bmatrix}3 & 1 \\\ 2 & 34\end{bmatrix}$ $\Rightarrow \, |A B| =\begin{bmatrix}1 & 1 \\\ 2 & 34\end{bmatrix}$ $=102-2$ $=100$