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Question
If for a square matrix A, A2 – A + I = 0, then A–1 equals ______.
Options
A
A + I
I – A
A – I
Solution
If for a square matrix A, A2 – A + I = 0, then A–1 equals I – A.
Explanation:
A2 – A + I = 0
A–1A2 – A–1A + A–1 = 0 ...(Multiplying by A–1)
A – I + A–1 = 0
A–1 = I – A
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