$S1:-$ The equation $AB=0$ doesn't necessarily imply that one of the matrices A and B must be Zero.
Example :- $A= \begin{bmatrix} 1 & 1\\ -1 & -1 \end{bmatrix}$
$B= \begin{bmatrix} -1 & -1\\ 1 & 1 \end{bmatrix}$
$AB= \begin{bmatrix} 0 & 0\\ 0 & 0 \end{bmatrix}$
Here both A and B are not $Zero$ matrices but Multiplication of $A$ and $B$ is $ZERO$.
Hence,$S1$ is False Statement.
$S2:-$ If product of A and B ( (i.e) AB ) = A , then B should be an identity matrix.
Example:- $A=\begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}$
$B=\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$
$AB=\begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}=A$
Hence,Statement $S2$ is True.