Show That Matrices Form a Group: \mathcal{D}_{m',m}^{(j)}

[ag_swe]

Homework Statement

Show that the matrices \mathcal{D}_{m',m}^{(j)}=\langle j,m'|\exp(-\frac{i}{\hbar}\vec{J}\hat{n}\Phi)|j,m\rangle form a group (i.e. multiplication, inverse and identity). No idea how to even begin.

 

[dextercioby]

What happens if you choose the axis of rotation \displaystyle{\hat{n}=\hat{k}}, with k along Oz and unit modulus ?