Answer
See below
Work Step by Step
Given $A$ and $B$ are $n × n$ matrices and $A$ is invertible,
then $A^{-1}$ exists
and $AA^{-1}=I=A^{-1}A$
Now let $x \in$ nullity (AB):
we have $ABx=0\\
\rightarrow A^{-1}ABx=A^{-1}.0\\
\rightarrow Bx=0\\
\rightarrow x \in nullity (B)\\
\rightarrow nullity (AB) \subseteq nullity (B)$
Let $y \in nullity (B)$
we have $By=0\\
\rightarrow Aby=A.0=0\\
\rightarrow y \in nullity(AB)\\
\rightarrow nullity (B) \subseteq nullity (AB)$
Hence, $nullity(AB) = nullity(B)$
