If A = begin{bmatrix} 1 & 1 1 & 1 end{bmatri | vedclass

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

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

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