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+1 vote
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in Mathematics by (63.5k points)

For the matrix A = [(1, 1, 1), (1, 2, -3), (2, -1, 3)], Show that A3 – 6A2 + 5A + 11 I = O. Hence, find A–1.

1 Answer

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by (64.8k points)
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Best answer

Given that

∴ A3 - 6A2 + 5A + 11I

∴ A-1 exist

Now, A3 - 6A2 + 5A + 11I = 0

⇒ AA(AA-1) - 6A(AA-1) + 5(AA-1) + 11(IA-1) = 0

⇒ AAI - 6AI + 5I + 11A-1 = 0

⇒ A2 - 6A + 5I = - 11A-1

⇒ A-1 = -  1/11(A2 - 6A + 5I)

⇒ A-1 = 1/11(-A2 + 6A - 5I)

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