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If A2 – A + I = 0, then the inverse of the matrix A is (A) A – I (B) I – A (C) A + I (D) A

If A2 – A + I = 0, then the inverse of the matrix A is
(A) A – I (B) I – A (C) A + I (D) A

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2 Answers

Arun
25750 Points
3 years ago
Dear 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 TU
14149 Points
3 years ago
 
Given that A2 – A + I = 0
If we multiply both sides by A-1 we have,
A-1 (A2 – A + I) = A-1 .0 = 0
Hence, A – I + A-1 = 0
This gives A-1 = -(A – I)
= I – A.

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