Consider the following matrices,
$A=\left[\begin{array}{ccc}2& -3& -5\\ -1& 4& 5\\ 1& -3& -4\end{array}\right]; B=\left[\begin{array}{ccc}1& -3& -4\\ -1& 3& 4\\ 1& -3& -4\end{array}\right]; C=\left[\begin{array}{ccc}0& 1& -1\\ 4& -3& 4\\ 3& -3& 4\end{array}\right]$
Which one of the following matrices posses an inverse?

$\left|A\right|=|\begin{array}{ccc}2& -3& -5\\ -1& 4& 5\\ 1& -3& -4\end{array}|=0\Rightarrow \text{\hspace{0.17em}A is singular }$

$\left|B\right|=|\begin{array}{ccc}1& -3& -4\\ -1& 3& 4\\ 1& -3& -4\end{array}|=0\Rightarrow \text{\hspace{0.17em}B is also singular}$

$\left|C\right|=|\begin{array}{ccc}0& 1& -1\\ 4& -3& 4\\ 3& -3& 4\end{array}|=-1\Rightarrow C\text{is non singular}$

Let,  $X=B{C}^2\Rightarrow \det .X=0$

$$\begin{gathered} Y=A^2{C}^2\Rightarrow \det .Y=0 \\ Z=A^{2}B\Rightarrow \det .Z=0 \end{gathered}$$

But  $W=C^3\Rightarrow \det .W\ne 0$

Hence  $C^3$ has an inverse