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If A={bmatrix} 1 & 2 & 2 2 & 1 & 2 2 & 2 & 1 {bmatrix}, find

Question

If $A = ⎣ ⎡ 122212221 ⎦ ⎤$ , find $A^{- 1}$
and hence prove that $A^{2} - 4 A - 5 I = 0$

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Asher Discussed

A = ⎣ ⎡ 122212221 ⎦ ⎤

, find

A^{- 1}

and hence prove that

A^{2} - 4 A - 5 I = 0

13 mins ago

Discuss this question LIVE

13 mins ago

Text solutionVerified

First find

A^{- 1}

A^{- 1} = \frac{1}{5} ⎣ ⎡ - 3 22 2 - 3 2 22 - 3 ⎦ ⎤

5 A^{- 1} = ⎣ ⎡ 1 - 4 22 2 1 - 4 2 22 1 - 4 ⎦ ⎤ = ⎣ ⎡ 122212221 ⎦ ⎤ - ⎣ ⎡ 400040004 ⎦ ⎤

5 A^{- 1} = A - 4 I

5 A^{- 1} = \times A = A \times A - 4 I \times A

5 I = A^{2} - 4 A

A^{2} - 4 A - 5 I = 0

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Question Text	If $A = ⎣ ⎡ 122212221 ⎦ ⎤$ , find $A^{- 1}$ and hence prove that $A^{2} - 4 A - 5 I = 0$
Answer Type	Text solution:1
Upvotes	150