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sage: Z = matrix(2,2)
sage: print Z.parent()

Full MatrixSpace of 2 by 2 dense matrices over Integer Ring

What you want is a matrix over the Symbolic Ring

sage: Z = matrix(SR,2,2)
sage: print Z.parent()
sage: Z[0,0] = sqrt(5)
sage: print Z

Alternatively a matrix over a Real Field

sage: Z = matrix(RR,2,2)
sage: print Z.parent()
sage: Z[0,0] = sqrt(5)
sage: print Z

sage: Z = matrix(2,2)
sage: print Z.parent()

Output:

Full MatrixSpace of 2 by 2 dense matrices over Integer Ring
Ring

That means your matrix can contain only Integers. What you want is a matrix over the Symbolic Ring Ring:

sage: Z = matrix(SR,2,2)
sage: print Z.parent()
sage: Z[0,0] = sqrt(5)
sage: print Z

Alternatively a matrix over a Real FieldField:

sage: Z = matrix(RR,2,2)
sage: print Z.parent()
sage: Z[0,0] = sqrt(5)
sage: print Z