Question

If $A=\left[\begin{array}{cc}1& 2\\ 2& 3\end{array}\right]$ and $B=\left[\begin{array}{cc}1& 1\\ 0& 0\end{array}\right]$ then what is determinant of AB ?

• A. $0$
• B. $1$
• C. $10$
• D. $20$

Answer 1

Answer: (A)

$0$

Given $A=\left[\begin{array}{cc}1& 2\\ 2& 3\end{array}\right]$ and $B=\left[\begin{array}{cc}1& 1\\ 0& 0\end{array}\right]$

$A\times B=\left[\begin{array}{cc}1& 2\\ 2& 3\end{array}\right]\times \left[\begin{array}{cc}1& 1\\ 0& 0\end{array}\right]=\left[\begin{array}{cc}1\times 1+2\times 0& 1\times 1+2\times 0\\ 2\times 1+3\times 0& 2\times 1+3\times 0\end{array}\right]=\left[\begin{array}{cc}1& 1\\ 2& 2\end{array}\right]$

$|A\times B|=\left|\begin{array}{cc}1& 1\\ 2& 2\end{array}\right|=2\times 1-2\times 1=0$