Past exam of the computer science course of the University of Oxford / 2019 / Quantum information / 1 / b / i

The columns are $i|+⟩$ and $-i|-⟩$. Their norms are one and their inner product is zero, since $|+⟩,|-⟩$ are orthonormal. Thus $M_1$ is a unitary matrix. Equivalently,using the Hadamard gate and Pauli Z gate. The different column phases do not destroy orthonormality.