When I run this code
import sympy as sp
sp.init_printing(pretty_print=False)
I = sp.Identity(3)
A = sp.MatrixSymbol('A',3,3)
A*I
I*A
sp.adjoint(A)*I
I*sp.adjoint(A)
I get the expected results,
A
A
Adjoint(A)
Adjoint(A)
However, if I run
sp.adjoint(I)*A
I get
Adjoint(I)*A
Why doesn't Sympy replace Adjoint(I) by I ?
Adjoint(MatrixExpr) doesn't evaluate, it is simply a symbolic object: https://github.com/sympy/sympy/blob/master/sympy/matrices/expressions/adjoint.py.
So I assume sp.adjoint(I) uses lazy loading on any matrix to save on computation until it is actually necessary. Once the function is evaluated, then the adjoint gets computed and set to I.
Perhaps I.adjoint() does what you would expect.