GATE AG 2026 • Q14 MCQ • 1 Mark

Section 1: Engineering Mathematics

Linear Algebra

Subtopic: Matrices and determinants

Question Statement:

Two square matrices A and B of the same order are such that det[A·B] = −80 and det[A] = 5. Here A·B is the product of A and B. The value of det[Bᵀ] is

Options:

  • (A) −16
  • (B) −1/16
  • (C) −400
  • (D) 28

Official Answer Key:

A

Step-by-Step Solution & Explanation

Property 1 (multiplicative property of determinants): det(A·B) = det(A) · det(B) ⇒ det(B) = det(A·B)/det(A) = −80/5 = −16 Property 2 (transpose property): det(Bᵀ) = det(B) ⇒ det(Bᵀ) = −16

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