Unitary matrices have orthogonal (orthonormal) rows/columns.

Theorem. A matrix $U$ is unitary if and only if its columns (and rows) form an orthonormal set with respect to the standard inner product on $\mathbb{C}^n$.

For columns $u_1, u_2, \ldots, u_n$ of $U$:
$$\langle u_i, u_j \rangle = u_j^* u_i = \delta_{ij} = \begin{cases} 1 & i = j \\ 0 & i \neq j \end{cases}$$

Example. The columns of $U = \frac{1}{\sqrt{2}}\begin{pmatrix} 1 & 1 \\ 1 & -1 \end{pmatrix}$ are $u_1 = \frac{1}{\sqrt{2}}(1, 1)^T$ and $u_2 = \frac{1}{\sqrt{2}}(1, -1)^T$. We verify: $\langle u_1, u_1 \rangle = 1$, $\langle u_2, u_2 \rangle = 1$, $\langle u_1, u_2 \rangle = 0$.