(C) Given the equation: $A^2 - A + I = 0$Subtract $I$ from both sides: $A^2 - A = -I$Factor out $A$ from the left side: $A(A - I) = -I$Multiply both s

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(C) Given the equation: $A^2 - A + I = 0$Subtract $I$ from both sides: $A^2 - A = -I$Factor out $A$ from the left side: $A(A - I) = -I$Multiply both sides by $A^{-1}$ from the left: $A^{-1}A(A - I) = A^{-1}(-I)$Since $A^{-1}A = I$, we have: $I(A - I) = -A^{-1}$$A - I = -A^{-1}$Multiplying by $-1$ on both sides: $A^{-1} = -(A - I) = I - A$

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

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If $A$ is a non-singular matrix and $A^2 - A + I = 0$, then $A^{-1} = \dots$

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A
$A$
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 $A$ is a non-singular matrix and $A^2 - A + I = 0$, then $A^{-1} = \dots$

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