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If A is a square matrix such that A2 = I where I is the identity matrix, then what is A-1 equal to?

If A is a square matrix such that A2 = I where I is the identity matrix, then what is A-1 equal to? Correct Answer A

Concept:

 A × A-1 = I, where I is an identity matrix

 

Calculation:

Given: A → square matrix

A2 = I

To find A−1=?

Given A2 = I

⇒A × A = I

But, we know A × A-1 = I

Compare the above equations, we get

∴A−1 = A

Hence, option (3) is correct.

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