Why quantum gates are represented as Unitary

Quantum Gate is represented as Unitary

When we think back on normalize condition of quantum state,

\begin{bmatrix}
\alpha^* &  \beta^* 
\end{bmatrix}U^{\dagger}U\begin{bmatrix}
\alpha \\
\beta   
\end{bmatrix}=1

For this normalization condition to be satisfied for any quantum state, the matrix must have the following property, namely, be unitary:

U^{\dagger}U=I, \space UU^{\dagger}=I