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Define the example in the question and call it a:

sage: a = CoxeterGroup(['A20']).gens()[0]

It displays as

sage: a
[-1  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0]
[ 0  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0]
[ 0  0  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0]
[ 0  0  0  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0]
[ 0  0  0  0  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0]
[ 0  0  0  0  0  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0]
[ 0  0  0  0  0  0  1  0  0  0  0  0  0  0  0  0  0  0  0  0]
[ 0  0  0  0  0  0  0  1  0  0  0  0  0  0  0  0  0  0  0  0]
[ 0  0  0  0  0  0  0  0  1  0  0  0  0  0  0  0  0  0  0  0]
[ 0  0  0  0  0  0  0  0  0  1  0  0  0  0  0  0  0  0  0  0]
[ 0  0  0  0  0  0  0  0  0  0  1  0  0  0  0  0  0  0  0  0]
[ 0  0  0  0  0  0  0  0  0  0  0  1  0  0  0  0  0  0  0  0]
[ 0  0  0  0  0  0  0  0  0  0  0  0  1  0  0  0  0  0  0  0]
[ 0  0  0  0  0  0  0  0  0  0  0  0  0  1  0  0  0  0  0  0]
[ 0  0  0  0  0  0  0  0  0  0  0  0  0  0  1  0  0  0  0  0]
[ 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  1  0  0  0  0]
[ 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  1  0  0  0]
[ 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  1  0  0]
[ 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  1  0]
[ 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  1]

Define the same matrix starting from the identity matrix and modifying the first two entries; call that b:

sage: b = identity_matrix(20)
sage: b[0:2, 0:0] = (-1, 1)

Check that a and b define the same matrix:

sage: b == a
True

However b displays differently:

sage: b
20 x 20 dense matrix over Integer Ring
(use the '.str()' method to see the entries)

Get the fuller display of b, showing all its entries, using print:

sage: print(b)
[-1  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0]
[ 0  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0]
[ 0  0  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0]
[ 0  0  0  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0]
[ 0  0  0  0  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0]
[ 0  0  0  0  0  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0]
[ 0  0  0  0  0  0  1  0  0  0  0  0  0  0  0  0  0  0  0  0]
[ 0  0  0  0  0  0  0  1  0  0  0  0  0  0  0  0  0  0  0  0]
[ 0  0  0  0  0  0  0  0  1  0  0  0  0  0  0  0  0  0  0  0]
[ 0  0  0  0  0  0  0  0  0  1  0  0  0  0  0  0  0  0  0  0]
[ 0  0  0  0  0  0  0  0  0  0  1  0  0  0  0  0  0  0  0  0]
[ 0  0  0  0  0  0  0  0  0  0  0  1  0  0  0  0  0  0  0  0]
[ 0  0  0  0  0  0  0  0  0  0  0  0  1  0  0  0  0  0  0  0]
[ 0  0  0  0  0  0  0  0  0  0  0  0  0  1  0  0  0  0  0  0]
[ 0  0  0  0  0  0  0  0  0  0  0  0  0  0  1  0  0  0  0  0]
[ 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  1  0  0  0  0]
[ 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  1  0  0  0]
[ 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  1  0  0]
[ 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  1  0]
[ 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  1]

Let us explain this difference in display, and how to get the summary display for a.

Even though a and b have the same entries, they don't have the same "parent"; a is an element in a matrix group while b is an element in a matrix space.

sage: a.parent()
Finite Coxeter group over Integer Ring with Coxeter matrix:
20 x 20 dense matrix over Integer Ring
sage: b.parent()
Full MatrixSpace of 20 by 20 dense matrices over Integer Ring

The difference in display comes from a different implementation of the __repr__ method for elements of matrix groups and elements of matrix spaces: compare a.__repr__?? and b.__repr__??.

To get the summary version for a, one solution is to convert it to a matrix space element.

sage: c = matrix(a)
sage: c
20 x 20 dense matrix over Integer Ring
(use the '.str()' method to see the entries)

To get elements of matrix groups to consistently use the shorter display when they reach 20 rows, one would have to change the __repr__ method of matrix group elements.