divideByVariable  divide all columns by a (power of a) variable
Description
divideByVariable(m,v)  divide each column of the matrix 'm' by as high a power of the variable 'v' as possible.
divideByVariable(m,v,d)  divide each column of the matrix 'm' by as high a power of the variable 'v' as possible, but divide by no more than v^d.
i1 : R = ZZ/101[a..d]
o1 = R
o1 : PolynomialRing

i2 : m = matrix{{a*b, a^2*c}, {a*b^2, a^4*d}}
o2 =  ab a2c 
 ab2 a4d 
2 2
o2 : Matrix R < R

i3 : divideByVariable(m,a)
o3 = ( b c , 2)
 b2 a2d 
o3 : Sequence

i4 : divideByVariable(m,a,1)
o4 = ( b ac , 1)
 b2 a3d 
o4 : Sequence

We may eliminate this routine.
Caveat
You can only divide by a variable, not a monomial, and you have little control on what power will be divided. This routine is mostly used by the saturation commands as a fast internal way of dividing.
Ways to use divideByVariable :

divideByVariable(Matrix,RingElement)

divideByVariable(Matrix,RingElement,ZZ)