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If A, B are two square matrices such that AB=B, BA=A then A+B WHOLE POWER n =

If A, B are two square matrices such that AB=B, BA=A then A+B WHOLE POWER n =

Grade:12

2 Answers

Deepak Kumar Shringi
askIITians Faculty 4404 Points
5 years ago
(A+B)2=A2+B2+AB+BA
=A2+B2+B+A= 2(A+B)
(A+B)^n = n(A+B)
BECAUSE -

.
NOW B^2=BB
=(BA)B
=B(AB) (MATRIX MULTIPLICATION OBEYS ASSOCIATIVE LAW)
=BA
=B.
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13 Points
2 years ago
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