Question

Show that the matrix A is unitary where A = `[[alpha+igamma,-beta+idel],[beta+idel,alpha-igamma]]` is unitary if `alpha^2+beta^2+gamma^2+del^2=1` 

Answer 1

Given, A is Unitary 

Consider, 

Similarlly, 

Substituting (2),(3),(4)&(5) in (1), 

Comparing corresponding terms, we get, 

unitary if `alpha^2+beta^2+gamma^2+del^2=1`