Question

# If $${A}^{2}-A+I=0$$, then the inverse of the matrix $$A$$ is

A
AI
B
IA
C
A+I
D
A

Solution

## The correct option is A $$I-A$$Given, $${ A }^{ 2 }-A+I=0$$$$\Rightarrow { A }^{ 2 }-A=-I$$$$\Rightarrow { A }^{ 2 }{ A }^{ -1 }-A{ A }^{ -1 }=-I{ A }^{ -1 }$$$$\Rightarrow A-I=-{ A }^{ -1 }$$$$\Rightarrow { A }^{ -1 }=I-A$$Mathematics

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