Q13 of 127 Page 131

If a = [ cc 3&1 -1&2 ], show that A2 – 5A + 7I = O. Hence find A–1.

We have A2 = A.A = .

So A2 – 5A + 7I =


Hence A2 – 5A + 7I = 0


∴ A.A – 5A = -7I


Now post multiply with A-1


So A.A.A-1-5A.A-1 = -7I.A-1


→ A.I – 5I = -7I.A-1 {since A.A-1 = I}


A – 5I = -7A-1 {since X.I = X}



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