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Problem
Problem
Statement-1
If
A
A
A
and
B
B
B
are two matrices such that
A
B
=
B
,
B
A
=
A
AB = B, BA = A
A
B
=
B
,
B
A
=
A
, then
A
2
+
B
2
=
A
+
B
A^2 + B^2 = A + B
A
2
+
B
2
=
A
+
B
.
Statement-2
A
A
A
and
B
B
B
are idempotent matrices, then
A
2
=
A
,
B
2
=
B
A^2 = A, B^2 = B
A
2
=
A
,
B
2
=
B
.
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