# Exercise 2.52

The Hadamard gate is defined as

$$
H = \frac{1}{\sqrt{2}}\begin{pmatrix}
1 & 1 \\ 
1 & -1 
\end{pmatrix}
$$(eqn:2.52.1)

Thus, we could calculate 

$$
H^2  = \frac{1}{2}\begin{pmatrix}
1 & 1 \\ 
1 & -1 
\end{pmatrix}\begin{pmatrix}
1 & 1 \\ 
1 & -1 
\end{pmatrix} = \frac{1}{2}\begin{pmatrix}
2 & 0 \\ 
0 & 2 
\end{pmatrix} = I
$$(eqn:2.52.2)