Answer
4. Yes.
Work Step by Step
Recall the definition of determinant and use the concept of cofactors to evaluate the matrix:
$\begin{array}( \\|A|= \\ \\ \end{array}
\begin{vmatrix} 2 & 1 &0 \\0 & -2&4 \\0 & 1&-3\end{vmatrix} \begin{array}( \\= 2\\ \\ \end{array}\begin{vmatrix} -2 & 4 \\1 & -3\end{vmatrix} \begin{array}( \\-\\ \\ \end{array}\begin{vmatrix} 0 & 4 \\0 & -3\end{vmatrix}$
$|A|=2((-2)(-3)-4\times1)-(0(-3)-4(0))=4$
As $|A|\ne0$, the matrix should have an inverse.