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Question

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


A
AI
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B
IA
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C
A+I
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D
A
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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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