  We construct quantum invariants of 3-manifolds based on a $\mathfrak{sl}_3$
matrix dilogarithm proposed by Kashaev. This matrix dilogarithm is an
$\mathfrak{sl}_3$ analogue of the (cyclic) quantum dilogarithm used to define
Kashaev's invariants as well as Baseilhac and Benedetti's quantum hyperbolic
invariants. % In this article, we show that the $\mathfrak{sl}_3$ matrix
dilogarithm can be considered as a 6$j$-symbol associated to modules of a
quantum group related to $U_q(\mathfrak{sl}_3)$. Moreover, we show that the
quantum invariants aforementioned allow to define a $\mathfrak{sl}_3$ version
of Kashaev's invariants, opening a route to define a $\mathfrak{sl}_3$ version
of Baseilhac and Benedetti's quantum hyperbolic invariants.
