Question

If $A=\left[\begin{array}{ccc}1& 2& 3\\ 0& 4& 5\\ 0& 0& 1\end{array}\right]$, then $det\left(A^{-1}\right)$ is ________. (correct to two decimal places)

• A. 0.25

Answer 1

The correct option is A 0.25

|A| =$\left|\begin{array}{ccc}1& 2& 3\\ 0& 4& 5\\ 0& 0& 1\end{array}\right|=1\times 4\times 1=4$
Now $det\left(A^{-1}\right)=\frac{1}{det\left(A\right)}=\frac{1}{|A|}=\frac{1}{4}$

$=0.25$