Square matrices A,B of the same order satisfy (AB)=-80 and A=5. Find (BT).

GATE 2026 AG – Question 14

Engineering Mathematics · Linear Algebra · 1 mark · Multiple choice

Square matrices $A,B$ of the same order satisfy $\det(AB)=-80$ and $\det A=5$. Find $\det(B^T)$.

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Correct answer: (A) −16

Determinants multiply:$\det A\det B=-80$,so $\det B=-80/5=-16$. Transposition does not change a determinant, thus $\det(B^T)=-16$. **A**.

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