Key idea For an n×nn\times nn×n identity matrix InI_nIn: InA=A,AIn=AI_nA=A,\qquad AI_n=AInA=A,AIn=A This follows from the Kronecker delta identity: δik={1,i=k0,i≠k\delta_{ik}=\begin{cases}1,& i=k\\0,& i\ne k\end{cases}δik={1,0,i=ki=k