a=1,R(A) =1
det A
=|α1 α2 α3|
|a a 1|
=|a 1 a|
|1 a a|
=a^2+a^2+a^2-(1+a^3+a^3)
=-2a^3+3a^2-1
det A =0
2a^3-3a^2 +1 =0
(a-1)(2a^2-a -1 )=0
(a-1)(2a+1)(a-1)=0
a=1 or -1/2
ie
a=-1/2 R(A)=2