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GATE 2025 CS (CS2) – Question 14

Engineering Mathematics · Linear Algebra · 1 mark · Multiple choice

Let $L, M$, and $N$ be non-singular matrices of order 3 satisfying the equations $L^2 = L^{-1}$, $M = L^8$ and $N = L^2$.

Which ONE of the following is the value of the determinant of $(M - N)$?

  1. $0$
  2. $1$
  3. $2$
  4. $3$

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Show answer and explanation

Correct answer: (A) $0$

Explanation

$L^2 = L^{-1}$ gives $L^3 = I$. So $M = L^8 = L^2 = N$, hence $M - N = 0$ and its determinant is 0.