#### Question

If A is a square matrix such that A^{2} = I, then A^{−}^{1} 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

\[A^{- 1} A^2 = A^{- 1} I\]

\[ \Rightarrow A = A^{- 1} I\]

\[ \Rightarrow A = A^{- 1}\]

\[ \Rightarrow A = A^{- 1} I\]

\[ \Rightarrow A = A^{- 1}\]

Is there an error in this question or solution?

Solution 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.