I was reading about teleportation which had the following Bell counterpart in $N$ dimensions $|{\phi}>=\sum_{i=0}^{N-1}|i>|i>$. The next line was $$(U\otimes I)|\phi>=\sum_{i,j=0}^{N-1}|j>U_{ji}\otimes |i>=\sum_{i,j=0}^{N-1}|j>\otimes|i>U_{ij}^T= (I\otimes U^T)|\phi>$$
Here $U$ is unitary. Now I understand $(U\otimes I)=(I\otimes U)$. But the terms in between I am finding hard to grasp. Okay I understood the second part which was $|j>U_{ji}$, but the next equivalence I could not understand. How did the $U_{ji}$ got shifted on the $i$. Also should there be a $U^{\dagger}$ instead of Transpose.