If $A=[a_{ij}]$ be a square matrix of order n, then the correct statements are :
A. A is a symmetric matrix if and only if $A^T=A$
B. A is a skew-symmetric matrix if and only if $A^T=-A.$
C. If order of A is $n×n$, then order of $A^T$ is $m×n (m ≠n).$
D. If $\begin{bmatrix} 1 & 2 \\3 & 4\end{bmatrix}=\begin{bmatrix}1 & 2\\3 & 2x\end{bmatrix}, $ then $x=4 $.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → A, B only
(A) Yes, 'A' matrix is symmetric.
if, $A^T=A$
(B) Yes, 'A' matrix is skew-symmetric.
if, $A^T=-A$