Question

If $\begin{pmatrix}2&1\\ 3&2\end{pmatrix} A = \begin{pmatrix}1&0\\ 0&1\end{pmatrix}$, then the matrix a is

• A. $\begin{pmatrix}2&1\\ 3&2\end{pmatrix}$
• B. $\begin{pmatrix}2&-1\\ -3&2\end{pmatrix}$
• C. $\begin{pmatrix}-2&1\\ 3&-2\end{pmatrix}$
• D. $\begin{pmatrix}2&-1\\ 3&2\end{pmatrix}$

Answer 1

Answer: (B)

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