  The Additive-Multiplicative Matrix Channel (AMMC) was introduced by Silva,
Kschischang and K\"otter in 2010 to model data transmission using random linear
network coding. The input and output of the channel are $n\times m$ matrices
over a finite field $\mathbb{F}_q$. On input the matrix $X$, the channel
outputs $Y=A(X+W)$ where $A$ is a uniformly chosen $n\times n$ invertible
matrix over $\mathbb{F}_q$ and where $W$ is a uniformly chosen $n\times m$
matrix over $\mathbb{F}_q$ of rank $t$.
  Silva \emph{et al} considered the case when $2n\leq m$. They determined the
asymptotic capacity of the AMMC when $t$, $n$ and $m$ are fixed and
$q\rightarrow\infty$. They also determined the leading term of the capacity
when $q$ is fixed, and $t$, $n$ and $m$ grow linearly. We generalise these
results, showing that the condition $2n\geq m$ can be removed. (Our formula for
the capacity falls into two cases, one of which generalises the $2n\geq m$
case.) We also improve the error term in the case when $q$ is fixed.
