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Grade 12Algebra

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?

Profile image of rutu
9 Years agoGrade 12
Answers icon

2 Answers

Profile image of ravi
ApprovedApproved Tutor Answer9 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.
 
Profile image of ankit singh
5 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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