Question

By using properties of determinants prove the following :

Answer 1

how to type determinant here lol ?

Answer 2

det ?
lol

Answer 3

Just draw it

Answer 4

^damn, yes ! :p

Answer 5

= \[(1+a^2+b^2)^3\]

Answer 6

(NOTE: I still have no idea how to do this but...)
something tells me a negative sign is missing somewhere

Answer 7

Not sure if there's a faster way to do it (the determinant of a 3x3 matrix is super fun!):
http://www.mathworks.com/help/aeroblks/determinantof3x3matrix.html

Answer 8

Or not... forget what I said :)
Carry on~

Answer 9

lol

Answer 10

http://thejuniverse.org/PUBLIC/LinearAlgebra/LOLA/detDef/ops.html

Answer 11

You still need the answer ? I can solve it and bring the steps of you want

Answer 12

@vikrantg4 ?

Answer 13

proof *

Answer 14

what is the first step @Eyad

Answer 15

And So on ,With respect to the signs

Answer 16

Co-factor expansion... nice :)

Answer 17

@UnkleRhaukus

Answer 18

im sure that will work, but i think there is a nicer solution,