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If A^{2} + 3I =0 find A^{-1}.

Question

If $A^{2} + 3 I = 0$ find $A^{- 1}$ .

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A^{2} + 3 I = 0

find

A^{- 1}

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Text solutionVerified

Given that,

A^{2} + 3 I = 0

By multiplying on both sides with

A^{- 1}

we get,

A^{2} . A^{- 1} + 3 I . A^{- 1} = 0. A^{- 1}

A . (A . A^{- 1}) + 3 (I . A^{- 1}) = 0

A . I + 3 A^{- 1} = 0

A + 3 A^{- 1} = 0

3 A^{- 1} = 0 - A = - A

∴ A^{- 1} = \frac{1}{3} (- A)

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