Question: Solving equation system over the integers (mod m)

Hello, I have a set of equations, and I want to solve it over the integers (mod 13). But msolve command fails. Here is my code:

eq:={a4*a1-11, a4*a2-12, a4*a3-6, a5*a1-3, a5*a2-8, a5*a3-4, a6*a1-2, a6*a2-1, a6*a3-7};
msolve(eq,13);

It fails, but I can solve it manually. Here is a solution:

a4*a1 = 11 => a4:=1 and a1:=11

a4*a2 = 12 => a2:=12

a4*a3 = 6 => a3:=6

a5*a1 = 3 => a5:=3/11 mod 13 = 5

a5*a2 = 8 => a2:=8/5 mod 13 = 12

a5*a3 = 4 => a3:=4/5 mod 13 = 6

a6*a1 = 2 => a6:=2/11 mod 13 = 12

a6*a2 = 1 => 12*12 mod 13 = 1

a6*a3 = 7 => 12*6 mod 13 = 7

So, how can I solve this using maple?

Thanks in advance.