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 the value of Det.$\left(2A^9{B}^{-1}\right)$, is

• A. $2$
• B. $1$
• C. $-1$
• D. $-2$

Answer 1

Answer: (D)

$-2$

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

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

$|B|=\left|\begin{array}{cc}3& 1\\ 7& 3\end{array}\right|=2$

$|2A^9{B}^{-1}|=2^2|A{|}^9\frac{1}{|B|}$

$=4\times (-1)\times \frac{1}{2}$

$\therefore |2A^9{B}^{-1}|=-2$

Hence, option D.