By the Frenet frame: $\mathbf{b} = \mathbf{t}\times\mathbf{n}$. Therefore $\mathbf{t}\times\mathbf{b} = \mathbf{t}\times(\mathbf{t}\times\mathbf{n}) = (\mathbf{t}\cdot\mathbf{n})\mathbf{t} - (\mathbf{t}\cdot\mathbf{t})\mathbf{n} = 0 - \mathbf{n} = -\mathbf{n}$, since $\mathbf{t}\cdot\mathbf{n}=0$ (orthogonal) and $|\mathbf{t}|=1$.