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If A Is a Square Matrix Such That A2 = I, Then A−1 is Equal to - CBSE (Arts) Class 12 - Mathematics

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Question

If A is a square matrix such that A2 = I, then A1 is equal to _______ .

  • A + I

  • A

  • 0

  • 2A

Solution

A

\[\text{ Given: }\hspace{0.167em} A^2 = I\]

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?

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Solution If A Is a Square Matrix Such That A2 = I, Then A−1 is Equal to Concept: Determinant of a Square Matrix.
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