Significance of fixed effect coefficients in multinomial logistic regression

I am trying to do a multinomial logit regression, and I understand that the fixed effects coefficients are a bit difficult to interpret and that they can in some cases be 0 or negative but actually have the opposite effect on the probability of the dependent variable (and vice versa). So I looked at the predicted probabilities to see the actual direction of the effect. But can I still use the coefficients to see if the effect is significant, regardless of direction? Or do I calculate the significance from the predicted probabilties?