Pauli-Y gate

Pauli-$Y$ is $Y=\begin{pmatrix}0&-i\\ i&0\end{pmatrix}$, combining a bit flip with a phase. Directly: $Y|0\rangle = i|1\rangle$ and $Y|1\rangle = -i|0\rangle$, matching this record's basis-action check. Up to convention $Y = iXZ$ (equivalently $-iZX$), which is why it behaves as the "odd one out" when composing $X$ and $Z$. $Y$ is Hermitian and unitary with $Y^2 = I$, so like $X$ and $Z$ it is its own inverse — the identity this record's matrix square verifies. Its eigenstates $|{\pm}i\rangle = \frac{1}{\sqrt2}(|0\rangle \pm i|1\rangle)$ have eigenvalues $\pm1$ and correspond to a $\pi$ rotation of the Bloch sphere about the $y$-axis. The imaginary prefactors are invisible to a single computational-basis measurement but matter as soon as $Y$ acts inside a superposition where relative phase drives interference, e.g. inside $Y$-basis stabilizer measurements.