GATE 2020 MT – Question 65

Engineering Mathematics · Linear algebra and matrices · 2 marks · Numerical answer

M and N are 3×3 matrices with det(M) = −9 and det(N) = −14. Find det(NM), nearest integer.

Show answer and explanation

Correct answer: 126 to 126

Explanation

Determinants multiply under matrix multiplication: det(NM) = det(N)det(M). Thus (−14)(−9) = 126. This property does not require M and N to commute.

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