A={{-1,1,I},{2,0,3},{2 I,-2 I,2}}
B={{2,0,-I},{0,1,0},{I,3,2}}
A.B
B.A
%%-%
Transpose[A]
Conjugate[A]
ConjugateTranspose[A]
Tr[A]
Det[B]
Inverse[B]
           2      I               -I      2
Out[16]= {{-, -I, -}, {0, 1, 0}, {--, -2, -}}
           3      3               3       3

B.Inverse[B]
Out[17]= {{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}

In[18]:= Inverse[A]
Inverse::sing: Matrix {{-1, 1, I}, {2, 0, 3}, {2 I, -2 I, 2}} is singular.

a={{I},{2 I},{2}}
b={{2},{1-I},{0}}
A.a
ConjugateTranspose[a].b
Transpose[a].B.b
a.ConjugateTranspose[b]

T={{2,I,1},{-I,2,I},{1,-I,2}}
Det[T]
Tr[T]
Eigenvalues[T]
Eigenvectors[T]
Eigensystem[T]
