  Results of this paper concern $n$-determinants which we defined in the paper
\cite{jan}. In the paper \cite{jabo}, $2$-determinants are considered. In this
paper, we extend results from \cite{jabo} on $n$-determinants by proving that
Cassini, d'Ocagne, Catalan and Vajda identities may be extended to hold for
$n$-step Fibonacci numbers.
