Bug when testing if a matrix is in SR

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On sagemath 8.9, I find the behavior of SR with matrix a bit strange.

sage: M = matrix([[0, -1], [1, 0]])
sage: print(SR(M)+M)
[[ 0 -1]
[ 1  0]              -1]
[              1 [ 0 -1]
[ 1  0]]

What is the use of coercing a matrix to the symbolic ring if it cannot be used as a matrix afterward?

These two lines of code also both raise an attribute error:

sage: SR(M) == M
sage: M in SR
AttributeError: 'ComplexIntervalField_class_with_category' object has no attribute 'complex_field'

By itself, it is not very relevant, but some element constructors (e.g. lie_algebra) contain a line

if x in self.base_ring():
    do something

which means SR cannot be used as a base ring.

Is this a known bug?

A workaround would be to add a single line in SR.__contains__ to return false when x is matrix (or maybe there are case when a matrix is considered in SR, I don't know), but this would not solve the underlying issues.