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If A^2 - A + I = 0, then find the inverse of A.

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If $A^{2} - A + I = 0$ , then find the inverse of A.

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A^{2} - A + I = 0

, then find the inverse of A.

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Text solutionVerified

We have

A^{2} - A + I = 0

Pre-multiply both sides, by

A^{- 1}

, we get

A^{- 1} AA - A^{- 1} A + A I = 0

∴ A - I + A^{- 1} = 0

∴ A^{- 1} = I - A

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Question Text	If $A^{2} - A + I = 0$ , then find the inverse of A.
Answer Type	Text solution:1
Upvotes	150