Explain why the expressions for the \(n\)-boson identity operator \(\hat{I}_{n}\) in Eqs. (6.2.63) and (6.2.64) are identical and verify that \(\hat{I}_{n}\left|\mathbf{p}_{1} \cdots \mathbf{p}_{n}\rightangle=\left|\mathbf{p}_{1} \cdots \mathbf{p}_{n}\rightangle\) and \(\hat{I}_{n}\left|\mathbf{p}_{1} \cdots \mathbf{p}_{n} ; S_{o}\rightangle=\) \(\left|\mathbf{p}_{1} \cdots \mathbf{p}_{n} ; S_{o}\rightangle\) as required.