 Solution

In the ordered computational basis $|0⟩,|1⟩$, the Pauli X gate, Pauli Y gate, Pauli Z gate, Hadamard gate and T gate areIn the ordered two-qubit computational basis $|00⟩,|01⟩,|10⟩,|11⟩$, with the first qubit controlling the second, the controlled-NOT gate isHere the T gate uses the conventional representative with first diagonal entry one; another common representative differs only by a global phase.