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Statement 1: If and are two matrices such that and
MATHEMATICS · Subjective · CBSE · Mathematics · Matrices · Matrices
Problem
Statement 1: If
A
A
A
and
B
B
B
are two matrices such that
A
B
=
B
AB=B
A
B
=
B
and
B
A
=
A
BA=A
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; that is,
A
2
=
A
A^2=A
A
2
=
A
and
B
2
=
B
B^2=B
B
2
=
B
.
Related theory
Matrices
Matrix operations
Properties of matrix operations
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