Engineering Entrance ExamsIf A2 – A + I = 0, then the inverse of the matrix A is (A) A – I (B) I – A (C) A + I (D) A Ashwani sinha 12 Years agoGrade
Arun6 Years agoDear student A^2 – A + I = 0 pre multiply by A^-1 A – I + A^-1 = 0 hence A^-1 = I – A so option B is correct
Vikas TU6 Years ago Given that A2 – A + I = 0If we multiply both sides by A-1 we have,A-1 (A2 – A + I) = A-1 .0 = 0Hence, A – I + A-1 = 0This gives A-1 = -(A – I)= I – A.