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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

ConceptDeterminant of a Square Matrix

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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