If A^{-1} = begin{bmatrix} 2 & -3 -1 & 2 end | vedclass

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(C) We know that for any invertible matrices $A$ and $B$,the property $(AB)^{-1} = B^{-1} A^{-1}$ holds true.Given $A^{-1} = \begin{bmatrix} 2 & -3 \

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$\begin{bmatrix} 2 & -3 \ -7 & 11 \end{bmatrix}$

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(C) We know that for any invertible matrices $A$ and $B$,the property $(AB)^{-1} = B^{-1} A^{-1}$ holds true.Given $A^{-1} = \begin{bmatrix} 2 & -3 \ -1 & 2 \end{bmatrix}$ and $B^{-1} = \begin{bmatrix} 1 & 0 \ -3 & 1 \end{bmatrix}$.Substituting these values,we get:$(AB)^{-1} = B^{-1} A^{-1} = \begin{bmatrix} 1 & 0 \ -3 & 1 \end{bmatrix} \begin{bmatrix} 2 & -3 \ -1 & 2 \end{bmatrix}$Performing matrix multiplication:$= \begin{bmatrix} (1)(2) + (0)(-1) & (1)(-3) + (0)(2) \ (-3)(2) + (1)(-1) & (-3)(-3) + (1)(2) \end{bmatrix}$$= \begin{bmatrix} 2 + 0 & -3 + 0 \ -6 - 1 & 9 + 2 \end{bmatrix}$$= \begin{bmatrix} 2 & -3 \ -7 & 11 \end{bmatrix}$

If $A^{-1} = \begin{bmatrix} 2 & -3 \\ -1 & 2 \end{bmatrix}$ and $B^{-1} = \begin{bmatrix} 1 & 0 \\ -3 & 1 \end{bmatrix}$,then $(AB)^{-1} =$

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