Question 150529
if two rows of a determinant are interchanged, what is true of the resulting determinant?


The sign is changed.  

Illustration:

{{{abs(matrix(2,2,2,-7,-4,5))=2*5-(-7)*(-4)=10-28=-18}}}

{{{abs(matrix(2,2,-4,5,2,-7))=(-4)*(-7)*(-4)=28-10=18}}}

In general just for a 2x2 matrix.

{{{abs(matrix(2,2,a,b,c,d))=ad-bc}}}

{{{abs(matrix(2,2,c,d,a,b))=cb-da=bc-ad= -ad+bc=-(ad-bc) }}}

Edwin</pre>