matrix problem?

Method 1：
|1 a b|
|a 1 b|
|a b 1|
=1*1*1 + a*b*a + b*a*b - b*1*a - a*a*1 - 1*b*b
= 1 + a²b + ab² - ab - a² - b²
= (1 - a²) + (a²b - ab) + (ab² - b²)
= (1 - a)(1 + a) + ab(a - 1) + b²(a - 1)
= - (a - 1)(1 + a) + (a - 1)(ab + b²)
= (a - 1) [ - (1 + a) + (ab + b²) ]
= (a - 1) (ab - a + b² - 1)
= (a - 1) [ a(b - 1) + (b - 1)(b + 1) ]
= (a - 1) (b - 1) (a + b + 1)


Method 2：
http://s7.postimg.org/pggq3lgmx/image.png

left=
|1 a b|
|a 1 b|
|a b 1|
=1+ba^2+ab^2-b^2 -a^2-ab

right
=(a-1)(b-1)(a+b+1)
=(ab-a-b+1)(a+b+1)
=a^2 b+ab^2+ab-a^2-ab-a-ab-b^2-b+a+b+1
=1+ab-a^2-b^2+a^2 b+ab^2
=left