Question

If A is an orthogonal matrix, then determinant of A is

• A. det A = not exist
• B. det A = 0
• C. det A = $\pm 1$
• D. None of these

Hint:

If A is an orthogonal matrix, then determinant of A is

Answer 1

The Correct Option is C

Step 1: Concept
An orthogonal matrix $A$ satisfies $AA' = I$.
Step 2: Analysis
Taking the determinant on both sides: $|AA'| = |I|$. Since $|AA'| = |A||A'|$ and $|I| = 1$, we have $|A||A'| = 1$.
Step 3: Evaluation
Using the property $|A'| = |A|$, the equation becomes $|A|^2 = 1$.
Step 4: Conclusion
Solving for $|A|$, we get $|A| = \pm 1$.
Final Answer: (c)