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  • Need solution for rd sharma maths class 12 chapter adjoint and inverse of a matrix exercise multiple choice question question 20

Need solution for rd sharma maths class 12 chapter adjoint and inverse of a matrix exercise multiple choice question question 20

Answers (1)

option (c) I-A

Given:  A^{2}-A+I=0

Hint: use multiplication formula to find the answer

Solution:  A^{2}-A+I=0

I=A-A^{2}

I=A-A.A

Post – multiply both sides by A-1

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

Hence , option (c) is correct

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