Question Bank • QB_SUB_EM_0005 MCQ • 1 Mark

Section 1: Engineering Mathematics

Linear Algebra

Subtopic: Linear and orthogonal transformations

Question Statement:

A real square matrix $Q$ is called orthogonal if and only if:

Options:

  • (A) $Q^T Q = I$
  • (B) $Q^T = -Q$
  • (C) $Q^2 = Q$
  • (D) $Q = Q^T$

Answer Key:

A

Step-by-Step Solution & Explanation

By definition, a real square matrix $Q$ is orthogonal if $Q^T Q = Q Q^T = I$, meaning its columns and rows form an orthonormal basis.
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