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(A) Given $A = \begin{bmatrix} i & 1 \ 0 & i \end{bmatrix}$.First,calculate $A^2 = A 	imes A = \begin{bmatrix} i & 1 \ 0 & i \end{bmatrix} \begin{b

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$\begin{bmatrix} 1 & -4i \ 0 & 1 \end{bmatrix}$

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(A) Given $A = \begin{bmatrix} i & 1 \ 0 & i \end{bmatrix}$.First,calculate $A^2 = A 	imes A = \begin{bmatrix} i & 1 \ 0 & i \end{bmatrix} \begin{bmatrix} i & 1 \ 0 & i \end{bmatrix} = \begin{bmatrix} i^2 & i+i \ 0 & i^2 \end{bmatrix} = \begin{bmatrix} -1 & 2i \ 0 & -1 \end{bmatrix}$.Next,calculate $A^4 = A^2 	imes A^2 = \begin{bmatrix} -1 & 2i \ 0 & -1 \end{bmatrix} \begin{bmatrix} -1 & 2i \ 0 & -1 \end{bmatrix}$.$A^4 = \begin{bmatrix} (-1)(-1) + (2i)(0) & (-1)(2i) + (2i)(-1) \ (0)(-1) + (-1)(0) & (0)(2i) + (-1)(-1) \end{bmatrix} = \begin{bmatrix} 1 & -2i - 2i \ 0 & 1 \end{bmatrix} = \begin{bmatrix} 1 & -4i \ 0 & 1 \end{bmatrix}$.

If $A = \begin{bmatrix} i & 1 \\ 0 & i \end{bmatrix}$,then $A^4$ equals

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