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(C) Let $P = \begin{bmatrix} 2 & 1 \ 3 & 2 \end{bmatrix}$ and $Q = \begin{bmatrix} -3 & 2 \ 5 & -3 \end{bmatrix}$. The equation is $PAQ = I$,where $

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

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(C) Let $P = \begin{bmatrix} 2 & 1 \ 3 & 2 \end{bmatrix}$ and $Q = \begin{bmatrix} -3 & 2 \ 5 & -3 \end{bmatrix}$. The equation is $PAQ = I$,where $I$ is the identity matrix. Then $A = P^{-1} I Q^{-1} = P^{-1} Q^{-1} = (QP)^{-1}$. First,calculate $QP$: $QP = \begin{bmatrix} -3 & 2 \ 5 & -3 \end{bmatrix} \begin{bmatrix} 2 & 1 \ 3 & 2 \end{bmatrix} = \begin{bmatrix} (-3)(2) + (2)(3) & (-3)(1) + (2)(2) \ (5)(2) + (-3)(3) & (5)(1) + (-3)(2) \end{bmatrix} = \begin{bmatrix} 0 & 1 \ 1 & -1 \end{bmatrix}$. Now,find $A = (QP)^{-1}$. The determinant $|QP| = (0)(-1) - (1)(1) = -1$. $A = \frac{1}{-1} \begin{bmatrix} -1 & -1 \ -1 & 0 \end{bmatrix} = \begin{bmatrix} 1 & 1 \ 1 & 0 \end{bmatrix}$.

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

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