Question

If $A = \begin{bmatrix} 2 & 1 \\ 3 & 2 \end{bmatrix}$, $A \begin{bmatrix} -3 & 2 \\ 5 & -3 \end{bmatrix} = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$, then the value of matrix

• A. $\begin{bmatrix} 1 & 1 \\ 1 & 0 \end{bmatrix}$

Answer 1

Answer: (A)

$\begin{bmatrix} 1 & 1 \\ 1 & 0 \end{bmatrix}$

Answer 2

Given $MAN=I$ with $M=\begin{bmatrix}2&1\\3&2\end{bmatrix}$ and $N=\begin{bmatrix}-3&2\\5&-3\end{bmatrix}$, we compute $A=M^{-1}N^{-1}$. Finding $M^{-1}$ and $N^{-1}$ and then multiplying yields

$$A=\begin{bmatrix} 1 & 1 \\ 1 & 0 \end{bmatrix}.$$