Inverting a matrix over a modular integer ring

Suppose I create the matrix

 M:=matrix([[random()$PF(19) for i in 1..3] for j in 1..3])

Assuming the determinant is non-zero, then I can invert the matrix in the
finite field PF(19).  But suppose I enter

N:=matrix([[random()$ZMOD(20) for i in 1..3] for j in 1..3])

If the determinant is relatively prime to 20, then the inverse of N exists
over the ring ZMOD(20).  But division is not defined in ZMOD - so how do I
invert N?

Thanks,
Alasdair

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