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  4. If A=[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1] then A4=

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Q. If $A=\begin{bmatrix}1 & 1 & 1 & 1 \\ 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & 1\end{bmatrix}$ then $A^{4}=$

KCETKCET 2022

Solution:

since $A$ is $4 \times 4$ matrix
then $A^{n}=4^{n-1} A$
$\therefore A^{4}=4^{4-1} A=4^{3} A=64\, A$