Home › Previous year questions › GATE 2025 BM › Question 17GATE 2025 BM – Question 17 Engineering Mathematics · Linear Algebra · 1 mark · Multiple choice
A 3×3 matrix M has determinant 8. Multiply every element by −2. Find the new determinant.
−64 −16 8 64 Practise this question in The GATE Grind →
Show answer and explanation Correct answer: (A) −64
Explanation Scaling every entry by −2 scales each of the three rows by −2. A determinant is linear in each row, so the total multiplier is (−2)³=−8. New determinant is −8×8=−64, A.
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