If the matrix $\begin{bmatrix} 3 & a+b & 4\\2 & 0 & -1\\a-b & c & 5\end{bmatrix}$ is symmetric, then the value of a, b and c is given by :

$a=3, b=-1, c=-1$

The correct answer is Option (1) → $a=3, b=-1, c=-1$

Since, the matrix is symmetric, $A=A^T$

$⇒\begin{bmatrix} 3 & a+b & 4\\2 & 0 & -1\\a-b & c & 5\end{bmatrix}=\begin{bmatrix} 3 & 2 & a-b\\a+b & 0 & c\\4 & -1 & 5\end{bmatrix}$

$⇒a+b=2,a-b=4,c=-1$

Now, $a=3,b=-1,c=-1$