Let A be a square matrix. Then,
(A) $A+A^T$ is a symmetric matrix
(B) $A-A^T$ is a skew-symmetric matrix
(C) $AA^T$ is a skew-symmetric matrix
(D) $A^TA$ is a symmetric matrix
Choose the correct answer from the options given below :
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (A), (B), (D) Only
(A) $(A+A^T)^T=A^T+(A^T)^T$
$=A^T+A$
$=A+A^T$
$⇒(A+A^T)^T=A+A^T$
(B) $(A-A^T)^T=A^T-(A^T)^T$
$=A^T-A$
$=-(A-A^T)$
(D) $(A^TA)^T=A^T(A^T)^T$
$=A^TA$