Question

If \( A \) and \( B \) are square matrices of same order and \( A = A^T, B = B^T \), then \( (ABA)^T = \)

• A. \( BAB \)
• B. \( ABA \)
• C. \( ABAB \)
• D. \( AB^T \)
• E. \( (AB)^T \)

Hint:

Always reverse order when taking transpose of matrix products.

Answer 1

The Correct Option is B

Concept: Transpose rule: \[ (ABC)^T = C^T B^T A^T \]

Step 1: Apply transpose
\[ (ABA)^T = A^T B^T A^T \]

Step 2: Use given
\[ A^T = A,\quad B^T = B \]

Step 3: Substitute
\[ = A B A \]

Step 4: Final result
\[ \boxed{ABA} \]