Answer
0, No.
Work Step by Step
Evaluate the determinant with cofactors:
$\begin{array}( \\|A|= \\ \\ \end{array}
\begin{vmatrix} -2 & -3/2 &1/2\\2 &4 &0\\1/2 &2 &1 \end{vmatrix} \begin{array}( \\= -2\\ \\\end{array}
\begin{vmatrix} 4 &0\\2 &1 \end{vmatrix} \begin{array}( \\+\frac{3}{2} \\ \\\end{array}
\begin{vmatrix} 2 &0\\1/2&1 \end{vmatrix} \begin{array}( \\+\frac{1}{2} \\ \\\end{array}
\begin{vmatrix} 2 &4\\1/2 &2 \end{vmatrix}$
$|A|=(-2)(4)+\frac{3}{2}(2)+\frac{1}{2}(4-2)=0$
As $|A|=0$, the matrix does not have an inverse.