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We cannot show
Z
n
−
1
converges by assuming
Z
n
is always
nonsingular and converges in probability to a matrix
A
unless
A
is
nonsingular. As a simple example,
Z
n
1
0
0
n
−
1
→
1
0
0
0
≡
A
but
Z
n
−
1
1
0
0
n
does not converge.
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