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  • Explain Solution for RD Sharma Maths Class 12 Chapter 6 Adjoint and inverse of a Matrix Exercise very short answer type Question 20 maths textbook solution

Explain Solution for RD Sharma Maths Class 12 Chapter 6 Adjoint and inverse of a Matrix Exercise very short answer type Question 20 maths textbook solution

Answers (1)

VSQ : 20

Answer : A^{-1}=I-A

Given : A^{2}-A+I=0

Hint : Use pre-multiplication technique

Solution : A^{2}-A+I=0

A^{2}-A=-I

pre-multiplication by A^{-1} on both sides

$$ \begin{aligned} &A\left(A A^{-1}\right)-A A^{-1}=-I A^{-1} \\ &A-I=-A^{-1} \\ &A^{-1}=I-A \end{aligned}

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