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 $I$.
$A A^{-1}=A^{-1}A=I.$
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Observe the bottom row of A. All zeros.
This means that the third row in AB is going to have all zeros, so
$AB\neq I_{3}$
$A$ and $B$ are not inverses of each other.