Matrices are as follows reading left to right:

Question

X=MatrixForm{{0,1},{1,0}}
Y=MatrixForm{{0,-i},{i,0}}
Z=MatrixForm{{1,0},{0,-1}}
H=MatrixForm 1/sqrt(2){{1,1},{1,-1}}
S=MatrixForm{{1,0},{0,i}}
T=MatrixForm{{1,0},{0,exp(i(pi)/4)}}
v=MatrixForm{{alpha},{beta}}

Show by computation which of those matrices equals (1/sqrt(2))(X+Z) and which equals T^(2).

Answer 1

S = T^2
H = 1/√2 (X+Z)