Question

If $A^{-1}=\left[\begin{array}{cc}1& -2\\ -2& 2\end{array}\right]$, then what is $det\left(A\right)$ equal to ?

• A. $2$
• B. $-2$
• C. $1/2$
• D. $-1/2$

Answer 1

The correct option is D $-1/2$

$det\left(A^{-1}\right)=(1\times 2)-(-2)\times (-2)=2-4=-2$

As we know that,

$det\left(A^{-1}\right)=\frac{1}{det\left(A\right)}$

$\Rightarrow det\left(A\right)=\frac{1}{det\left(A^{-1}\right)}=\frac{1}{-2}=-\frac{1}{2}$