Find all values of a, b, and c for which A is symmetric.

I set this matrix equal to its transpose and used them both to make the following system of equations, and solved it by gaussian elimination

a - 2b + 2c = 3

2a + b + c = 0

a + c = -2

I got a = -18, b = 5, c = 31

How can I check if this is the right answer?