a,1,0,0
-1,b,1,0
0,-1,c,1
0,0,-1,d
r2+(1/a)r1:
a,1,0,0
0,(ba+1)/a,1,0
0,-1,c,1
0,0,-1,d
r3+[a/(ab+1)]r2:
a,1,0,0
0,(ba+1)/a,1,0
0,0,(cba+c+a)/(ba+1),1
0,0,-1,d
r4+[(ba+1)/(cba+c+a)]r3:
a,1,0,0
0,(ba+1)/a,1,0
0,0,(cba+c+a)/(ba+1),1
0,0,0,(dcba+dc+da+ba+1)/(cba+c+a)
=a*[(ba+1)/a]*[(cba+c+a)/(ba+1)]*[(dcba+dc+da+ba+1)/(cba+c+a)]
=ab+ad+cd+abcd+1