Proving det(AB) = det(A)det(B) for 2×2 matrices

[ilikephysics]

What is the following question asking?

Question:

Prove that the determinant of the product of two general 2x2 matrces is the product of their determinants.


What I think is that I should come up with two 2x2 matrices.
1 2 2 3 12 15
3 4 and 5 6 multiply them together and get 26 33

The determinant of the product matrix is six. The determinat of the first matrix is -2 and the second one is -3. Multiply -2 times -3 and that is 6. So I proved that the determinant of the product of the two matrices is the product of their determinants.

Is this right?

 

[ilikephysics]

here are the matrices

1 2 (1)
3 4

2 3
5 6 (2)

12 15
26 33 (product matrix)

 

[turin]

Originally posted by ilikephysics
What I think is that I should come up with two 2x2 matrices.
1 2 2 3 12 15
3 4 and 5 6 multiply them together and get 26 33
...
Is this right?

You should probably be more general (let the elements be letters instead of numbers, and then show it). It looks like you've got the right idea, though.