  In this paper the necessary and sufficient conditions for the product of
composition operators to be isometry are obtained on weighted Bergman space.
With the help of a counter example we also proved that unlike on
$\mathcal{H}^2(\mathbb{D})$ and $\mathcal{A}_{\alpha}^2(\mathbb{D}),$ the
composition operator on $\mathcal{S}^2(\mathbb{D})$ induced by an analytic self
map on $\mathbb{D}$ with fixed origin need not be of norm one. We have
generalized the Schwartz's well known result on
$\mathcal{A}_{\alpha}^2(\mathbb{D})$ which characterizes the almost
multiplicative operator on $\mathcal{H}^2(\mathbb{D}).$
