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Byju's Answer
Standard XII
Mathematics
Definition of a Determinant
If B is an id...
Question
If B is an idempotent matrix and
A
=
I
−
B
, then
A
A
2
=
A
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B
A
2
=
I
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C
A
B
=
O
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D
B
A
=
O
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Solution
The correct options are
A
A
2
=
A
C
A
B
=
O
D
B
A
=
O
Since,
B
is an idempotent matrix,
B
2
=
B
.....(1)
⇒
B
(
I
−
B
)
=
O
where
O
is a square matrix
Given
A
=
I
−
B
.....(2)
⇒
B
A
=
O
Multiplying (2) by
B
A
B
=
(
I
−
B
)
B
⇒
A
B
=
B
−
B
2
⇒
A
B
=
B
−
B
=
O
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1
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Q.
A square matrix
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