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You want to factor A's elements :

sage: A.apply_map(factor)
[                     a11                      a12                       b1]
[                       0 -(a12*a21 - a11*a22)/a11   -(a21*b1 - a11*b2)/a11]

(ask.agemath.org's Mathjiax interpreter won't display this matrix correctly...).

HTH,