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Solution for Let a Be a Square Matrix Such that a 2 − a + I = O , Then Write a − 1 Interms of A. - CBSE (Science) Class 12 - Mathematics

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Question

Let A be a square matrix such that \[A^2 - A + I = O\], then write \[A^{- 1}\]  interms of A.

Solution

\[\text{ Given: } A^2 - A + I = O\]
\[ A^{- 1} \left( A^2 - A + I \right) = A^{- 1} O (\text{ Pre - multiplying both sides because }A^{- 1}\text{ exists})\]
\[\left( A^{- 1} A^2 \right) - \left( A^{- 1} A \right) + A^{- 1} I = O  ( A^{- 1} O = O)\]
\[ \Rightarrow A - I + A^{- 1} = O ( A^{- 1} I = A^{- 1} )\]
\[ \Rightarrow A^{- 1} = I - A\]

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APPEARS IN

 R.D. Sharma Mathematics for Class 12 by R D Sharma (Set of 2 Volume) (2018-19 Session) (with solutions)
Chapter 8: Solution of Simultaneous Linear Equations
Q: 20 | Page no. 35

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Solution for question: Let a Be a Square Matrix Such that a 2 − a + I = O , Then Write a − 1 Interms of A. concept: Determinant of a Square Matrix. For the courses CBSE (Science), CBSE (Commerce), PUC Karnataka Science, CBSE (Arts)
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