If \(A = \begin{pmatrix} 1 & 2 \\ 2 & -1 \end{pmatrix} \) ,then which ONE of…

GATE · 2025 · CS · Set 2 · Computer Science & IT

If \(A = \begin{pmatrix} 1 & 2 \\ 2 & -1 \end{pmatrix} \) ,then which ONE of the following is \(A^8\) ?

A.
\(\begin{pmatrix} 25 & 0 \\ 0 & 25 \end{pmatrix} \)
B.
\(\begin{pmatrix} 125 & 0 \\ 0 & 125 \end{pmatrix} \)
C.
\(\begin{pmatrix} 625 & 0 \\ 0 & 625 \end{pmatrix} \)
D.
\(\begin{pmatrix} 3125 & 0 \\ 0 & 3125 \end{pmatrix} \)

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Correct answer: C

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