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(C) Given the diagonal matrix $A = \begin{bmatrix} 2 & 0 & 0 \ 0 & 1 & 0 \ 0 & 0 & 3 \end{bmatrix}$.Since $A$ is a diagonal matrix,its inverse $A^{-

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$\frac{11}{6}$

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(C) Given the diagonal matrix $A = \begin{bmatrix} 2 & 0 & 0 \ 0 & 1 & 0 \ 0 & 0 & 3 \end{bmatrix}$.Since $A$ is a diagonal matrix,its inverse $A^{-1}$ is also a diagonal matrix where the diagonal elements are the reciprocals of the diagonal elements of $A$.Thus,$A^{-1} = \begin{bmatrix} \frac{1}{2} & 0 & 0 \ 0 & \frac{1}{1} & 0 \ 0 & 0 & \frac{1}{3} \end{bmatrix}$.The sum of all elements of $A^{-1}$ is $\frac{1}{2} + 1 + \frac{1}{3}$.To add these,find the common denominator,which is $6$.Sum $= \frac{3}{6} + \frac{6}{6} + \frac{2}{6} = \frac{11}{6}$.

If $A = \begin{bmatrix} 2 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 3 \end{bmatrix}$,then the sum of all elements of $A^{-1}$ is . . . . . . .

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