If A is a square matrix such that A2 = A. Show that :-

(I + A)3 = 7A + I

  (I+A)3
=I3+A3+3AI(I+A)   
=I3+A3+3A(I+A)      {As, A I = A}
=I3+A3+3AI+3A2
=I+A2A+3A+3A2
=I+A.A+3A+3A       {As, A= A}
=I+A2+6A
=I+A+6A
=I+7A
Hence Proved

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