Matrices Practice Questions Ques24
Question: Which of the following matrices is always symmetric?
Options:
(A) $A + A^T$
(B) $A - A^T$
(C) $A \cdot A^T$
(D) Option (A) and Option (B)
Show Answer
Answer: D
Explanation:
(A) Correct. $A + A^T$ is always symmetric because $(A + A^T)^T = A^T + (A^T)^T = A^T + A = A + A^T$.
(B) Incorrect. $A - A^T$ is skew-symmetric, not symmetric.
(C) Correct. $A A^T$ is always a symmetric matrix for any matrix A.
(D) Correct.
BETA
