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sage: M = matrix(2,2,var('a b c d'))
sage: M;  M.parent(); M(a=5)

[a b]
[c d]
Full MatrixSpace of 2 by 2 dense matrices over Symbolic Ring
[5 b]
[c d]

We can use substitution M(a=5) (looking similar to a function call). What happens if we try to use M as variable of a function?

sage: M = matrix(2,2,var('a b c d'))
sage: print M.parent(); print
sage: f(M) = M.transpose()

The error message indicates that the type of M has changed.

Full MatrixSpace of 2 by 2 dense matrices over Symbolic Ring

Traceback (click to the left of this block for traceback)
...
AttributeError: 'sage.symbolic.expression.Expression' object has no attribute 'transpose'

M is no longer a matrix over SR but a symbolic expression.

sage: M.parent()

Symbolic Ring

When defining a symbolic function with a variable M, this M becomes (implicitly) a member of SR overwriting the previous definition of M. After redefining M as matrix:

sage: A = M[0,0] + M[1,1]
sage: A; A(a=5,b=3,c=0,d=-2)

a + d
3