(C) Given the equation: ${A^2} - A + I = 0$ Rearranging the terms to isolate $I$: $I = A - {A^2}$ Factor out $A$ from the right side: $I = A(I - A)$ M

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(C) Given the equation: ${A^2} - A + I = 0$ Rearranging the terms to isolate $I$: $I = A - {A^2}$ Factor out $A$ from the right side: $I = A(I - A)$ Multiply both sides by ${A^{-1}}$ from the left: ${A^{-1}}I = {A^{-1}}A(I - A)$ Since ${A^{-1}}A = I$ and ${A^{-1}}I = {A^{-1}}$: ${A^{-1}} = I(I - A)$ Therefore: ${A^{-1}} = I - A$

Class 12 Mathematics 3 and 4 .Determinants and Matrices Adjoint and inverse of matrices

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If ${A^2} - A + I = 0$,then ${A^{-1}} = $

AIEEE 2005 All AIEEE

A
${A^{-2}}$
B
$A + I$
C
$I - A$
D
$A - I$

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3 and 4 .Determinants and Matrices

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Adjoint and inverse of matrices

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If ${A^2} - A + I = 0$,then ${A^{-1}} = $

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