[QUE/QM-20009]

Consider two  particles, $A,B$ each having spin 1. Construct all possible states $\vert{SM}\rangle$ with definite values of $S^2$ and $S_z$. Use the notation $\vert{A  m_1}\rangle\vert{B    m_2}\rangle$ to represent the states of the two particles having definite $z-$ projections $m_1,m_2$ of spin. Verify that the states are symmetric under exchange of $m_1$ and $m_2$ when total spin is $S=2,0$ and antisymmetric for $S=1$.