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If A and B are two matrices such that AB=A and BA=B then B 2 =? Cant we write it as equal to both A 2 and B 2 ? If not why?

If A and B are two matrices such that  AB=A and BA=B then B2=?
 
Cant we write it as equal to both  A 2  and B2 ?
If not why?

Grade:12

2 Answers

ravi
24 Points
7 years ago
 Dear rutu, Given that AB=A AND BA=B.
NOW B^2=BB
=(BA)B
=B(AB)  (MATRIX MULTIPLICATION OBEYS ASSOCIATIVE LAW)
=BA
=B.
 
ankit singh
askIITians Faculty 614 Points
3 years ago
as BA=B,THAN A =I,AS AB=B THAN B=I
THERFORE B^2=B  OR
NOW B^2=BB
=(BA)B
=B(AB)  (MATRIX MULTIPLICATION OBEYS ASSOCIATIVE LAW)
=BA
=B
.REGARDS ANKIT SINGH

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