Question

If $A,B$ and $C$ are $n\times n$ matrix and $det\left(A\right)=2,det\left(B\right)=3$ and $det\left(C\right)=5$, then the value of $[det(A^{2}B{C}^{-1}\left)\right]$ is
(where $[\cdot ]$ represents the greatest integer function)

Answer 1

Given: $|A|=2,|B|=3,|C|=5,$
Now, $det\left(A^{2}B{C}^{-1}\right)=|A^{2}B{C}^{-1}|=\frac{|A{|}^2|B|}{|C|}=\frac{4\times 3}{5}=\frac{12}{5}$
$\therefore [det(A^{2}B{C}^{-1}\left)\right]=\left[\frac{12}{5}\right]=2$