If the matrix $A=\left[\begin{array}{rcr}3 & 2 a & -5 \\ -4 & 0 & b \\ -5 & 3 & 7\end{array}\right]$ is symmetric then the value of (a + b) is

1

Let $A=\left[\begin{array}{rcr}3 & 2 a & -5 \\ -4 & 0 & b \\ -5 & 3 & 7\end{array}\right]$

⇒ A is symmetric matrix, so, A = A'

$\left[\begin{array}{rcr}3 & 2 a & -5 \\ -4 & 0 & b \\ -5 & 3 & 7\end{array}\right]$=$\left[\begin{array}{rcr}3 & -4 & -5 \\ 2a & 0 & 3 \\ -5 & b & 7\end{array}\right]$

2a = -4,    b = 3

$a = \frac{-4}{2}$

a = -2

∴ a + b = -2 + 3 = 1