Mathematics - Determinant Question with Solution | TestHub

Let $|A|=a,|B|=b$ $\Rightarrow \mid A^{\eta }\rceil =a\left|A^{-1}\right|=\frac{1}{a},\left|B^{\eta }\right|=b,\left|B^{-1}\right|=\frac{1}{b}$ $\because AB{A}^{\eta }=8\Rightarrow |A||B|\mid A^{\eta }-8\dots (1)$ $\Rightarrow a\cdot b\cdot a=8\Rightarrow a^{2}b=8$ $\because A{B}^{-1}|=8\Rightarrow H|\left|B^{-1}\right|=8\Rightarrow a,\frac{1}{b}=8$ From (1) \& (2) $a=4,b=\frac{1}{2}$ Then, $\left|B{A}^{-1}{B}^{\eta }\right|=|B|\left|A^{-1}\right|\left|B^{\eta }\right|=b\cdot \frac{1}{a}\cdot b=\frac{b^2}{a}=\frac{1}{16}$