If $A$ and $B$ are two square matrices with $\operatorname{det} A=5$ and $\operatorname{det}\left(B^T \cdot A^T\right)=-15$, then $\operatorname{det} B$ is equal to

Question

Aicharya · Accepted Answer

Given, $|A|=5 ;\left|B^T A^Tight|=-15$ We know $|A|=\left|A^Tight|$ $\begin{aligned} 	herefore \quad\left|B^Tight|\left|A^Tight| & =|B||A|=-15 \ |B| & =\frac{-15}{|A|}=\frac{-15}{5}=-3\end{aligned}$

If $A$ and $B$ are two square matrices with $\operatorname{det} A=5$ and $\operatorname{det}\left(B^T \cdot…

Solution