i am given 2 matrices A= a1 b1 c1 a2 b2 c1 a3 b3 c3 B= -c2 3c1 -c3 b2 -3b1 b3 -5a2 15a1 -5a3 and also given is: 5detA+detB=10 what i need to fin is det(3A2B-1) what i did to help me was det(3)=27 det(A2)=detA*detA det(B-1)=1/detB i see that if i perform 2 "swaps" on B, once between R1 and R3 , and then between C1 and C2, these actions wont change detB. now i can divide my new R1 by 5, and my new c1 by 3 and transpose B to get a new B* , detB=(5*3)detB* now my new matrix B* is ALMOST identical to A, except for the (-) signs before some of its numbers, which are drivin me mad, how can i get rid of them, if i can get rid of them i can find detA. any ideas? have all my steps beeen legal??