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GATE 2021 CE (CE2) – Question 14

Engineering Mathematics · Linear Algebra: Matrix algebra, systems of linear equations, eigenvalues and eigenvectors · 1 mark · Multiple choice

For an orthogonal square matrix A, which condition is mandatory?

  1. $AA^T=I$
  2. $AA^T=0$
  3. $AA^T=A^{-1}$
  4. $AA^T=A^2$

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Show answer and explanation

Correct answer: (A) $AA^T=I$

Explanation

Orthogonality means the columns form an orthonormal basis, hence $A^TA=I$. A square orthogonal matrix has inverse $A^{-1}=A^T$, which also implies $AA^T=I$. Therefore **A** is the defining identity.