Answer
$A$ and $B$ are not inverses of each other.
Work Step by Step
The inverse of an $n\times n$ matrix $A$ is that $n\times n$ matrix $A^{-1}$ which,
when multiplied by $A$ on either side, yields the $n\times n$ identity matrix $I$.
$A A^{-1}=A^{-1}A=I.$
---
$AB=\left[\begin{array}{ll}
2 & 0\\
0 & 3
\end{array}\right]\left[\begin{array}{ll}
1/2 & 0\\
0 & 1/2
\end{array}\right]=\left[\begin{array}{ll}
1+0 & 0+0\\
0+0 & 0+3/2
\end{array}\right]=\left[\begin{array}{ll}
1 & 0\\
0 & 3/2
\end{array}\right]\neq I_{2}$
$A$ and $B$ are not inverses of each other.