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(D) Given $A = \begin{bmatrix} 1 & a \ 0 & 1 \end{bmatrix}$.Calculate $A^2$:$A^2 = A \cdot A = \begin{bmatrix} 1 & a \ 0 & 1 \end{bmatrix} \begin{bm

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$\begin{bmatrix} 1 & 4a \ 0 & 1 \end{bmatrix}$

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(D) Given $A = \begin{bmatrix} 1 & a \ 0 & 1 \end{bmatrix}$.Calculate $A^2$:$A^2 = A \cdot A = \begin{bmatrix} 1 & a \ 0 & 1 \end{bmatrix} \begin{bmatrix} 1 & a \ 0 & 1 \end{bmatrix} = \begin{bmatrix} 1(1)+a(0) & 1(a)+a(1) \ 0(1)+1(0) & 0(a)+1(1) \end{bmatrix} = \begin{bmatrix} 1 & 2a \ 0 & 1 \end{bmatrix}$.Calculate $A^3$:$A^3 = A \cdot A^2 = \begin{bmatrix} 1 & a \ 0 & 1 \end{bmatrix} \begin{bmatrix} 1 & 2a \ 0 & 1 \end{bmatrix} = \begin{bmatrix} 1 & 3a \ 0 & 1 \end{bmatrix}$.Calculate $A^4$:$A^4 = A \cdot A^3 = \begin{bmatrix} 1 & a \ 0 & 1 \end{bmatrix} \begin{bmatrix} 1 & 3a \ 0 & 1 \end{bmatrix} = \begin{bmatrix} 1 & 4a \ 0 & 1 \end{bmatrix}$.Thus,$A^4 = \begin{bmatrix} 1 & 4a \ 0 & 1 \end{bmatrix}$.

If $A = \begin{bmatrix} 1 & a \\ 0 & 1 \end{bmatrix}$,then $A^4$ is equal to

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