If matrix $A=\begin{bmatrix}1 & 0 & 0\\0& 1& 0\\0 & 1 & 1\end{bmatrix}, B =\begin{bmatrix} 0 & 0 & 2\\0 & 2 & 0\\2 & 0 & 0\end{bmatrix}, C=\begin{bmatrix}1 & 0 & 1\\0 & 0 & 1\\1 & 1 & 0 \end{bmatrix}, D=\begin{bmatrix} 0 & 0\\0 & 0\\0 & 0\end{bmatrix}$ then which of the following is true ?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → C is a symmetric matrix
A symmetric matrix is always,
$A=A^T$
$⇒C=\begin{bmatrix}1 & 0 & 1\\0 & 0 & 1\\1 & 1 & 0 \end{bmatrix}=C^T=\begin{bmatrix}1 & 0 & 1\\0 & 0 & 1\\1 & 1 & 0 \end{bmatrix}$