Question

If A is a square matrix then orthogonality property mandates

• A. \( A A^T = I \)
• B. \( A A^T = 0 \)
• C. \( A A^T = A^{-1} \)
• D. \( A A^T = A^2 \)

Hint:

An orthogonal matrix satisfies the condition \( A A^T = I \), which implies that its inverse is equal to its transpose.

Answer 1

The Correct Option is A

If \( A \) is an orthogonal matrix, it satisfies the property: \[ A A^T = I, \] where \( I \) is the identity matrix. This property is the defining characteristic of orthogonal matrices, meaning the rows and columns of \( A \) are orthonormal vectors.
Final Answer: \( A A^T = I \)