Reference frame as a $(1,1)$-tensor field $R$ with $R^2=R$

In a paper about the splitting of the space-time [for reference "THE STRUCTURE OF SPACE–TIME: RELATIVITY GROUPS" (International Journal of Geometric Methods in Modern Physics Vol. 3, No. 3 (2006) 591–603)], it identifies the reference frame with a $(1,1)$-tensor field $Rinmathcal{T}^1_1(M)$, $M$ is the space-time, and satisfying the condition $R^2=R$. For convenience, it decompose $R$ into the tensor product of a vector field $Gamma$ and a one-form $alpha$
$$R=alpha otimes Gamma$$
and the requirement $R^2=R$ is equivalent to the condition $alpha[Gamma]=1$.

My question is: how do I prove this last equivalence? I have no clue about how to compute $R^2$.