# Math Help - Prove the identity

1. ## Prove the identity

I don't understand this:

Prove the identity without evaluating the determinants.

$\left|\begin{matrix}a_1&b_1&a_1+b_1+c_1\\a_2&b_2&a _2+b_2+c_2\\a_3&b_3&a_3+b_3+c_3\end{matrix}\right| =\left|\begin{matrix}a_1&b_1&c_1\\a_2&b_2&c_2\\a_3 &b_3&c_3\end{matrix}\right|$

It's a question at the end of a section of properties of determinant functions, but I don't know how to do it

2. See here for a very similar thread. Columns versus rows makes little difference to a determinant.

3. Thank you! I get it now.

4. You're welcome. Have a good one!

5. The determinant on the left is the sum of three determinants two of which have identical columns and are therefore zero.