Questions
If AB = A and BA = B, where A c. · B are square matrices, then
a
B2=B and A2=A
b
B2≠B and A2=A
c
A2≠A,B2=B
d
A2≠A,B2≠B
detailed solution
Correct option is A
We have,A2=AA⇒ A2=(AB)A [∵AB=A]⇒ A2=A(BA) ⇒ A2=AB [∵BA=B]⇒ A2=A [∵AB=A]and,B2=BB⇒B2=(BA)B [∵BA=B]⇒B2=B(AB)⇒B2=BA [∵AB=A]⇒B2=B [∵BA=B]Talk to our academic expert!
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