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

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$2^9 A$

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(B) Given $A = \begin{bmatrix} 1 & 1 \ 1 & 1 \end{bmatrix}$.First,calculate $A^2 = A 	imes A = \begin{bmatrix} 1 & 1 \ 1 & 1 \end{bmatrix} \begin{bmatrix} 1 & 1 \ 1 & 1 \end{bmatrix} = \begin{bmatrix} 1+1 & 1+1 \ 1+1 & 1+1 \end{bmatrix} = \begin{bmatrix} 2 & 2 \ 2 & 2 \end{bmatrix} = 2A$.Now,calculate $A^3 = A^2 	imes A = (2A) 	imes A = 2(A^2) = 2(2A) = 2^2 A$.Similarly,$A^4 = A^3 	imes A = (2^2 A) 	imes A = 2^2 (A^2) = 2^2 (2A) = 2^3 A$.By induction,we can generalize that $A^n = 2^{n-1} A$.For $n = 10$,$A^{10} = 2^{10-1} A = 2^9 A$.

If $A = \begin{bmatrix} 1 & 1 \\ 1 & 1 \end{bmatrix}$,then $A^{10} = $ . . . . . . .

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