It's known that the Hadamard operation is just a rotation of the sphere about the $\hat{y}$ axis by 90 degrees, followed by a rotation about the $\hat{x}$ axis by 180 degrees.
On the other hand, $H^{2}=I$, where $H$ is the unitary matrix corresponding to the Hadamard gate and $I$ is the identity matrix.
If we do the rotation corresponding to the Hadamard matrix twice, then based on $H^{2}=I$, we would come out to the original situation, right? But, somehow, I can not see that. Could someone shed some light on this problem?
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