If A is a square matrix x , such that A 2 = I , then A - 1 is equal to:

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Solution

Q.
If A is a square matrix $x,$ such that $A^{2} = I,$ then $A^{- 1}$ is equal to:

1 2A

2 0

3 A

4 A + 1

Ans.
(3)

Ans. A

Explanation:

   $A^{2} = I$

then    $A \cdot A = I$

or $A^{- 1} (A \cdot A) = A^{- 1} I$

$\Rightarrow$ $(A^{- 1} A) A = A^{- 1}$

$\Rightarrow$    $I A = A^{- 1}$

$\Rightarrow$ $A^{- 1} = A$

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