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Solution for If a is a Square Matrix Such that A2 = I, Then A−1 is Equal to (A) a + I (B) a (C) 0 (D) 2a - CBSE (Science) Class 12 - Mathematics

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Question

If A is a square matrix such that A2 = I, then A1 is equal to
(a) A + I
(b) A
(c) 0
(d) 2A

Solution

(b) A
\[\text{ Given: }\hspace{0.167em} A^2 = I\]
\[\text{ Given: }\hspace{0.167em} A^2 = I\]
On multiplying both sides by
\[A^{- 1}\] , we get

\[A^{- 1} A^2 = A^{- 1} I\]
\[ \Rightarrow A = A^{- 1} I\]
\[ \Rightarrow A = A^{- 1}\]
  Is there an error in this question or solution?

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: 22 | Page no. 38

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Solution for question: If a is a Square Matrix Such that A2 = I, Then A−1 is Equal to (A) a + I (B) a (C) 0 (D) 2a concept: Determinant of a Square Matrix. For the courses CBSE (Science), CBSE (Arts), PUC Karnataka Science, CBSE (Commerce)
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