Let $\displaystyle M=(g_{i, j})$ by a symmetric matrix. Then is it true in general that $\displaystyle u^t M v = v^t M u$ for $\displaystyle u$ and $\displaystyle v$ column vectors?

If not, when is it true?

(I'm trying to show that $\displaystyle <u, v>=u^t M v$ forms an inner product, but as far as I can see $\displaystyle <u, v> \neq <v, u>$...)