If A is an identity matrix of order 3, then its inverse (A^-1)

Question

Question

This question was previously asked in

NDA (Held On: 21 Apr 2019) Maths Previous Year paper

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Answer 1

Concept

If A is any matrix of order n and it’s inverse exists, then we can write

AA^-1 = A^-1A = I, where I = Identity matrix of order n

Calculation

Given: A is an identity matrix of order 3 i.e. A = I

Multiplying both sides by A^-1 we get

⇒ AA^-1 = IA^-1

⇒ I = A^-1 [∵ A matrix multiplied by the identity matrix is the matrix itself i.e. AI = A]

⇒ A = A^-1