A square matrix A is called orthogonal if_______ where A’ is the transpose of A.

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Question

This question was previously asked in

NDA (Held On: 9 Sept 2018) Maths Previous Year paper

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Answer 1

Concept:

Orthogonal matrix: When the product of a matrix to its transpose gives identity matrix.

Suppose A is a square matrix with real elements and of n x n order and A^T or A’ is the transpose of A.

AA^T = I

Calculation:

Suppose A is a square matrix with real elements and of n x n order and A^T or A’ is the transpose of A.

Then according to the definition;

AA^T = I

Pre multiplication by A^-1

A^-1 AA^T = A^-1 I

IA^T = A^-1

A^T = A^-1 or A’ = A^-1
then A is orthogonal matrix.

∴ Option 2 is correct