Special case
If the matrices are an irreducible representation of a group , and if
(1)
for all in , then , where is identity matrix [Ham89, sec.3.14].
General case
Let be a group, and two finite-dimensional irreducible -modules. Then any intertwiner
(2)
satisfies
- ,
- , .
The second option is exactly what you've seen above [, FH91, sec.1.2].