Find a and b so that 1, 2a, 3; 8, 4, b + 1; 3, 7, 6 is symmetric.

Step 1. First pair. $a_{12} = 2a$ and $a_{21} = 8$, so $2a = 8$ and $a = 4$.

Step 2. Second pair. $a_{23} = b + 1$ and $a_{32} = 7$, so $b = 6$.

Step 3. The other pair. $a_{13} = 3$ and $a_{31} = 3$ already agree.