- #1
digipony
- 35
- 0
Homework Statement
Prove the relation det(AB)=det(A)det(B)
Homework Equations
det A = [itex]\sum_{k}A_{kq} C_{kq}[/itex]
The Attempt at a Solution
Here is what I have done:
(detA)(detB)= [itex]\sum_{k}A_{kq} C_{kq}[/itex] [itex]\sum_{k}B_{kq} C_{kq}[/itex]
= [itex]\sum_{k}(A_{kq}B_{kq}) C_{kq}[/itex]
= [itex]\sum_{k}(AB)_{kq} C_{kq}[/itex]
=det(A+B)
My question is: is it mathematically proper to factor out the Ckq in the summation, or am I breaking some matrix/summation rule here?
Thanks!
Last edited: