If A is a non-singular matrix and A²-A+I=0, then A^{-1}=.

Correct Answer is : I−AI-AI−A

Correct Answer is : I−AI-AI−A

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MHTCET 17 Apr 2026 Shift 1 Paper

Question : 116 of 150

Marks: +1, -0

A

A^{2}-A+I=0

A^{-1}=\ldots

Solution:

Concept:

Since

A

is non-singular,

A^{-1}

exists and can be used to simplify the given matrix equation.

Explanation:

The given equation is

A^{2}-A+I=0

Multiply both sides by

A^{-1}

on the left:

A^{-1}(A^{2}-A+I)=A^{-1}\cdot 0

This gives:

A^{-1}A^{2}-A^{-1}A+A^{-1}I=0

Now simplify each term:

A^{-1}A^{2}=A,\quad A^{-1}A=I,\quad A^{-1}I=A^{-1}

Substitute these into the equation:

A-I+A^{-1}=0

Rearrange to isolate

A^{-1}

A^{-1}=I-A

Answer:

A^{-1}=I-A

Hence, the correct option is C. $I-A$ .

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