A sum in determinants...need help....

Code:

`|(a+b-c) (-c+a-b) (a+b+c) |`

| (a-c) (c-a) (b-a) | = (a+b-c)(-c+a-b)(a-c)

| (a-b) (a-c) (a+b) |

using properties of determinants without expanding the determinant

I tried a lot of ways like with following steps C(3) -> C(3) + C(2) , R(1) -> R(1) + R(2) ,

R(1) -> R(1) + R(2) - R(3).....but i could get nothing...its not my homework sum....i am just a 6th grade maths enthusiast.....i saw this sum somewhere.....i tried to solve this but couldnt get.......can anyone help me up to solve this......or atleast guide me.......where C(1) means column 1 and R(1) means Row 1 and similar things to that

Re: A sum in determinants...need help....

Can you check for typo's ? As a way of checking the result I substituted values for a,b and c.

a=1,b=1,c=0 yields different results (-2 and zero) for the determinant and the RHS.