Answer
False
Work Step by Step
Assume that $A=\begin{bmatrix}
1 & 0 \\ 0 & 0
\end{bmatrix}$ $B=\begin{bmatrix}
0 & 0 \\ 0 & 1
\end{bmatrix} $are an $n × n$ matrices
We can see $rank (A)=rank (B)=1\\
\rightarrow nullity (A)=nullity (B)=1\\
\rightarrow AB=\begin{bmatrix}
0 & 0\\ 0 & 0
\end{bmatrix}\\
\rightarrow rank(AB)=0\\
\rightarrow nullity (AB)=2$
Since $nullity (AB)=2 \ne 1 =nullity A.nullity B$
Hence, the statement is false.
