# Homework Help: Determinant functions

1. Nov 22, 2008

### FourierX

1. The problem statement, all variables and given/known data

Let A be a 3 x 3 matrix. Consider the function f(A) = a11a22a33; g(A) = a11 a12 a13 and h(A) =1. Show that each of these is not a determinant function.

2. Relevant equations

det(I) = 1
det(B) = det(A) (if B is obtained from adding a mutiple of one row of A to another row)
det(B) = - det(A) (if B is obtained from interchange two rows)
det(B) = m det(A) (if B obtained from A by multiplying a row of A by the number m)

3. The attempt at a solution
isn't f(A) = a11a22a33 a determinant function ?

2. Nov 22, 2008

### naresh

Can you show that all four conditions are satisfied for f(.)?

3. Nov 22, 2008

### FourierX

what to take as a reference, though?

4. Nov 22, 2008

### naresh

I don't understand what you mean by reference. You should be able to show that for any arbitrary matrix A= aij, if you do the things stated in the four conditions, f(.) behaves as a determinant function.

To prove that f(.) is not a determinant function, a counterexample will suffice. Trying to prove that f() is a determinant function might help you come up with this counter-example.

5. Nov 23, 2008

### FourierX

I understand determinants with numbers. but its confusing with variables. Can you give me a simple example please?

6. Nov 23, 2008