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Question

Consider the following statement :
A: If AB=A and BA=Bthen An+Bn=A+B
R:A and B are idempotent matrices.
Then the correct option is

A
Both statements A and R are True and R is correct explanation of A.
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B
Both A and R are True but R is not correct explanation to A
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C
A is true R is False
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D
A is false R is true
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Solution

The correct option is A Both statements A and R are True and R is correct explanation of A.
Reason
A2=A.A=AB.A
=A.B.A
=A.B
=A

Similarly, B2=B
Hence, A and B are idempotent.
An+Bn=A+B
So, Both statements are true and R is correct explanation to A.

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