Discussion
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
Answer: A
The value is \(-16\).
The determinant of a product is the product of the determinants, and transposing a matrix does not change its determinant:
\[ \begin{aligned} \det(AB) &= \det A \cdot \det B \\ -80 &= 5 \det B \\ \det B &= -16 = \det B^{T} \end{aligned} \]
\(-\frac{1}{16}\) is \(1/\det B\), the determinant of the inverse. \(-400\) comes from multiplying \(-80\) by 5 instead of dividing, and 28 has no basis in the rules above.
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