`a_r={cos((2rpi)/9)+isin((2rpi)/9)}` where `r in {1,2,3 . . . 9}`
Find the value of `abs((a_1,a_2,a_3),(a_4,a_5,a_6),(a_7,a_8,a_9))`

If a_(r)="cos"(2rpi)/9+i "sin"(2rpi)/9 then value of the determinant Delta=|(1,a_(8),a_(7)),(a_(3),a_(2),a_(1)),(a_(6),a_(5),a_(4))| is

Evaluate: /_\ |[1+a_1, a_2, a_3],[a_1, 1+a_2, a_3],[a_1, a_2, 1+a_3]|

If a_i,i=1,2,....,9 are perfect odd squares, then |[a_1,a_2,a_3],[a_4,a_5,a_6],[a_7,a_8,a_9]| is always a multiple of

If a_r=(cos2rpi+is in2rpi)^(1//9) , then prove that |a_1a_2a_3a_4a_5a_6a_7a_8a_9|=0.

If alpha_r=(cos2rpi+isin2rpi)^(1/10) , then |(alpha_1, alpha_2, alpha_4),(alpha_2, alpha_3, alpha_5),(alpha_3, alpha_4, alpha_6)|= (A) alpha_5 (B) alpha_7 (C) 0 (D) none of these

If a_i>0, i=1, 2, 3,..., n then prove that a_1/a_2+a_2/a_3+a_3/a_4+...+a_(n-1)/a_n+a_n/a_1gen .