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(C) Given $A = \begin{bmatrix} a & 0 & 0 \ 0 & b & 0 \ 0 & 0 & c \end{bmatrix}$.Calculate $A^2 = A 	imes A = \begin{bmatrix} a & 0 & 0 \ 0 & b & 0

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$\begin{bmatrix} a^n & 0 & 0 \ 0 & b^n & 0 \ 0 & 0 & c^n \end{bmatrix}$

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(C) Given $A = \begin{bmatrix} a & 0 & 0 \ 0 & b & 0 \ 0 & 0 & c \end{bmatrix}$.Calculate $A^2 = A 	imes A = \begin{bmatrix} a & 0 & 0 \ 0 & b & 0 \ 0 & 0 & c \end{bmatrix} \begin{bmatrix} a & 0 & 0 \ 0 & b & 0 \ 0 & 0 & c \end{bmatrix} = \begin{bmatrix} a^2 & 0 & 0 \ 0 & b^2 & 0 \ 0 & 0 & c^2 \end{bmatrix}$.Similarly,$A^3 = A^2 	imes A = \begin{bmatrix} a^2 & 0 & 0 \ 0 & b^2 & 0 \ 0 & 0 & c^2 \end{bmatrix} \begin{bmatrix} a & 0 & 0 \ 0 & b & 0 \ 0 & 0 & c \end{bmatrix} = \begin{bmatrix} a^3 & 0 & 0 \ 0 & b^3 & 0 \ 0 & 0 & c^3 \end{bmatrix}$.By the principle of mathematical induction,for any positive integer $n$,we have $A^n = \begin{bmatrix} a^n & 0 & 0 \ 0 & b^n & 0 \ 0 & 0 & c^n \end{bmatrix}$.Thus,the correct option is $C$.

If $A = \begin{bmatrix} a & 0 & 0 \\ 0 & b & 0 \\ 0 & 0 & c \end{bmatrix}$,then $A^n = $

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