(* DETERMINANTE DI UNA MATRICE *)

Clear[a];
a={{1,2,0,-1,2},{-1,1,6,-2,0},{2,4,8,-5,-1},{3,-4,9,6,0},{-2,0,-7,4,0}};
MatrixForm[a]

m15={{-1,1,6,-2},{2,4,8,-5},{3,-4,9,6},{-2,0,-7,4}};
m35={{1,2,0,-1},{-1,1,6,-2},{3,-4,9,6},{-2,0,-7,4}};
MatrixForm[m15]
MatrixForm[m35]
Det[a]
a[[1]][[5]]*Det[m15]+a[[3]][[5]]*Det[m35]