DQ 1: The determinant has many nice properties. Two are:

1. det(AB) = det(A)det(B)
2. A is singular if det(A) = 0
   Use this to argue that AB is singular if A is singular or B is singular.
   (Please answer it with 135 words and one example, one reference)

DQ 2: Which of the following are true? Justify your answer.

1. If A is singular, then adj(A) is singular.
2. If adj(A) is singular, then A is singular.
3. If A is not singular, then adj(A) is not singular.
4. A is singular if adj(A) is singular.