Question
Question: If A<sup>2</sup> – A + I = 0, then the inverse of A is –...
If A2 – A + I = 0, then the inverse of A is –
A
A + I
B
A
C
A – I
D
I – A
Answer
I – A
Explanation
Solution
A2 – A + I = 0
A–1(A2 – A + I) = 0
A2A–1 – A–1A + A–1I = 0
AI – I + A–1 = 0
A – I + A–1 = 0
A–1 = I – A