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Inverse of a Matrix

If A2-3A=I,...

Question

If $A^{2} - 3 A = I, t h e n A^{- 1}$ =.....

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Solution

Given that $A^{2} - 3 A = I$
multiply both sides $A^{- 1}$ on both sides
$A^{- 1} (A^{2} - 3 A) = I A^{- 1}$
$∴$ $A^{- 1} = A - 3 A^{- 1} . A$
$= A - 3 I$
$A^{- 1} = A - 3 I$

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