Question

Let the matrix $A$ and $B$ be defined as $A=\left[\begin{array}{cc}3& 2\\ 2& 1\end{array}\right]$ and $B=\left[\begin{array}{cc}3& 1\\ 7& 3\end{array}\right]$ then find the value of Det$\left(2A^9{B}^{-1}\right)$

Answer 1

$A=\left|\begin{array}{cc}3& 2\\ 2& 1\end{array}\right|=3-4=-1$ and

$B=\left[\begin{array}{cc}3& 1\\ 7& 3\end{array}\right]=9-7=2$

$\left|2A^9{B}^{-1}\right|=\frac{2{\left|A\right|}^9}{\left|B\right|}=\frac{2\times {(-1)}^9}{2}=-1$