Question

If $\left(\begin{array}{cc}2& 1\\ 3& 2\end{array}\right)A=\left(\begin{array}{cc}1& 0\\ 0& 1\end{array}\right)$, then the matrix a is

• A. $\left(\begin{array}{cc}2& 1\\ 3& 2\end{array}\right)$
• B. $\left(\begin{array}{cc}2& -1\\ -3& 2\end{array}\right)$
• C. $\left(\begin{array}{cc}-2& 1\\ 3& -2\end{array}\right)$
• D. $\left(\begin{array}{cc}2& -1\\ 3& 2\end{array}\right)$

Answer 1

Answer: (B)

We know that if $BA=AB=I$, then $A$ and $B$ are inverse of each other. Let $B=\left(\begin{array}{cc}2& 1\\ 3& 2\end{array}\right)$
$\Rightarrow |B|=1$
$adj(B)=\left(\begin{array}{cc}2& -1\\ -3& 2\end{array}\right)$
$B^{-1}=\left(\begin{array}{cc}2& -1\\ -3& 2\end{array}\right)$
$\therefore A=B^{-1}=\left(\begin{array}{cc}2& -1\\ -3& 2\end{array}\right)$