What is the Binomial Formula in Matrices without Evaluating Determinants?

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Homework Statement



I'm sorry this doesn't look too nice but it is supposed to be two matricces.

Show:

|1 a1-b1 a1+b1| |1 a1 b1|
|1 a2-b2 a2+b2|=2*|1 a2 b2|
|1 a3-b3 a3+b3| |1 a3 b3|

without evaluating the determinants.

Homework Equations



The Attempt at a Solution



It pretty obviously has got something to do with the 3. binomial formula and the rule that λ*A = λ*every value in the matrix.

I really don't know where to start on this, since I can't evaluate the determinants.
I'm pretty sure there is an easy way to do this, but I just can't see it.

Help is very much appreciated!

Thank you
 
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Welcome to PF!

Hi Crution! Welcome to PF! :smile:

Do you know any rules for adding one column to another column? :wink:
 
thanks that was enough help :-)
 

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