The products of involutions in a matrix centralizer

A square matrix $A$ is an involution if $A^{2} = I$. The centralizer of a $S$ denoted by $\mathscr{C}(S)$ the set all such that $AS SA$ over algebraically closed field characteristic not equal to 2. We determine necessary and sufficient conditions for $A \in \mathscr{C}(S)$ be product involutions in where basic Weyr with homogeneous structure length 3. Finally, we will show some results case when greater than