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Question
If A is a square matrix such that A2 = I, then A−1 is equal to _______ .
Options
A + I
A
0
2A
Solution
A
\[\text{ Given: }\hspace{0.167em} A^2 = I\]
On multiplying both sides by
\[A^{- 1}\] , we get
\[A^{- 1} A^2 = A^{- 1} I\]
\[ \Rightarrow A = A^{- 1} I\]
\[ \Rightarrow A = A^{- 1}\]
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