  Let $(g_{n})_{n\geq 1}$ be a sequence of independent and identically
distributed positive random $d\times d$ matrices and consider the matrix
product $G_n: = g_n \ldots g_1$. Under suitable conditions, we establish the
Berry-Esseen bounds on the rate of convergence in the central limit theorem and
moderate deviation expansions of Cram\'er type, for the matrix norm $\| G_n \|$
of $G_n$, for its $(i,j)$-th entry $G_n^{i,j}$, and the and for its spectral
radius $\rho(G_n)$.
