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(C) Given the diagonal matrix $A = \begin{bmatrix} 2 & 0 & 0 \ 0 & 3 & 0 \ 0 & 0 & 4 \end{bmatrix}$.Since $A$ is a diagonal matrix,its inverse $A^{-

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$\begin{bmatrix} \frac{1}{4} & 0 & 0 \ 0 & \frac{1}{9} & 0 \ 0 & 0 & \frac{1}{16} \end{bmatrix}$

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(C) Given the diagonal matrix $A = \begin{bmatrix} 2 & 0 & 0 \ 0 & 3 & 0 \ 0 & 0 & 4 \end{bmatrix}$.Since $A$ is a diagonal matrix,its inverse $A^{-1}$ is given by the reciprocal of its diagonal elements:$A^{-1} = \begin{bmatrix} \frac{1}{2} & 0 & 0 \ 0 & \frac{1}{3} & 0 \ 0 & 0 & \frac{1}{4} \end{bmatrix}$.Now,we need to find $(A^{-1})^2 = A^{-1} 	imes A^{-1}$:$(A^{-1})^2 = \begin{bmatrix} \frac{1}{2} & 0 & 0 \ 0 & \frac{1}{3} & 0 \ 0 & 0 & \frac{1}{4} \end{bmatrix} 	imes \begin{bmatrix} \frac{1}{2} & 0 & 0 \ 0 & \frac{1}{3} & 0 \ 0 & 0 & \frac{1}{4} \end{bmatrix} = \begin{bmatrix} \frac{1}{4} & 0 & 0 \ 0 & \frac{1}{9} & 0 \ 0 & 0 & \frac{1}{16} \end{bmatrix}$.Thus,the correct option is $C$.

For matrix $A = \begin{bmatrix} 2 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 4 \end{bmatrix}$,$(A^{-1})^2 = $ . . . . . .

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