Question 1044576
{{{abs(matrix(5,5,a,b,c,d,1,b,c,d,a,1,c,d,a,b,1,d,a,b,c,1,b,a,d,c,1))}}}.

Perform the following elementary column operations (ECO3) IN SUCCESSION (which don't change the value of the determinant):

{{{1*C[1] + C[4]}}},
{{{1*C[2] + C[4]}}},
{{{1*C[3] + C[4]}}}.

What you get is the determinant

{{{abs(matrix(5,5,a,b,c,a+b+c+d,1,b,c,d,a+b+c+d,1,c,d,a,a+b+c+d,1,d,a,b,a+b+c+d,1,b,a,d,a+b+c+d,1))}}}.

={{{(a+b+c+d)abs(matrix(5,5,a,b,c,1,1,b,c,d,1,1,c,d,a,1,1,d,a,b,1,1,b,a,d,1,1))=0}}},

since columns 4 and 5 have identical entries.  (Note that a+b+c+d was factored ONCE only from the fourth column.)