for A being Matrix of 3,REAL holds Det A = (((((((A * (1,1)) * (A * (2,2))) * (A * (3,3))) - (((A * (1,3)) * (A * (2,2))) * (A * (3,1)))) - (((A * (1,1)) * (A * (2,3))) * (A * (3,2)))) + (((A * (1,2)) * (A * (2,3))) * (A * (3,1)))) - (((A * (1,2)) * (A * (2,1))) * (A * (3,3)))) + (((A * (1,3)) * (A * (2,1))) * (A * (3,2)))