Here are some comments on some of the problems you handed in

Sec. 3.1: 

12c. There is only one nonzero term in the defining formula for the determinant and it 
comes from the permutation 3214 with 3 inversions. So the determinant is -2x3x6x5

Sec 3.2: 

14. use the product rule: the product of the dets of A abd B is 1 so neither can be 0

15. (a) A times A inverse is I and det of A inverse is the reciprocal of the det of A
    Use the product rule again.
    (b) A and A transpose have the same det  and use the product rule again

17 Use the product rule again!

3.3:

16. Use formula (3) on page 161

17. Use the are formula on page 162 along with the matrix giving the transformation
   along with formula 5 on page 62

3.4:

13. Use A times adjA =det(A)I_n.  so if A is singular A times adj (A)=O.So if adj(A) 
were nonsingular, then multiplying by its inverse we get A=O. But if A=O, adj(A) =O 
and cannot be nonsingular.

14. Use the above equation and the product rule.