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For matrix A if AA^T = I, I is identity matrix then A is?

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For matrix A if AA^T = I, I is identity matrix then A is?

(a) Orthagonal  matrix

(b) Nilpotent matrix

(c) Idempotent matrix

(d) None of the mentioned

The question was posed to me in an international level competition.

This intriguing question comes from Types of Matrices in chapter Basic Structures: Sets, Functions, Sequences, Sums and Matrices of Discrete Mathematics

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Best answer
The correct option is (a) Orthagonal  matrix

Best explanation: For orthagonal matrices AA^T = I = A^T A.

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