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GATE 2025 CS (CS2) – Question 11

Engineering Mathematics · Linear Algebra · 1 mark · Multiple choice

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

  1. $\begin{pmatrix}25 & 0\\0 & 25\end{pmatrix}$
  2. $\begin{pmatrix}125 & 0\\0 & 125\end{pmatrix}$
  3. $\begin{pmatrix}625 & 0\\0 & 625\end{pmatrix}$
  4. $\begin{pmatrix}3125 & 0\\0 & 3125\end{pmatrix}$

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Show answer and explanation

Correct answer: (C) $\begin{pmatrix}625 & 0\\0 & 625\end{pmatrix}$

Explanation

$A^2 = 5I$, so $A^8 = (A^2)^4 = 5^4 I = 625I$.