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+i sin 2rpi)^(19) , then prove that |[a_1,a_2,a_3],[a_4,a_5,a_6],[a_7,a_8,a_9]|=0 .

If a_r=(cos2rpi+i sin 2rpi)^(1//9) , then prove that |[a_1,a_2,a_3],[a_4,a_5,a_6],[a_7,a_8,a_9]|=0 .

If a_1, a_2, a_3,54,a_6,a_7, a_8, a_9 are in H.P., and D=|[a_1,a_2,a_3],[5, 4,a_6],[a_7,a_8,a_9]| , then the value of [D]i sw h e r e[dot] represents the greatest integer function

If a_1, a_2, a_3,54,a_6,a_7, a_8, a_9 are in H.P., and D=|[a_1,a_2,a_3],[5, 4,a_6],[a_7,a_8,a_9]| , then the value of [D]i sw h e r e[dot] represents the greatest integer function

Suppose a_1, a_, are real numbers, with a_1!=0. If a_1, a_2,a_3, are in A.P., then (a) A=[(a_1,a_2,a_3),(a_4,a_5,a_6),(a_5,a_6,a_7)] is singular (where i=sqrt(-1)) (b)The system of equations a_1x+a_2y+a_3z=0,a_4x+a_5y+a_6z=0,a_7x+a_8y+a_9=0 has infinite number of solutions. (c) B=[(a_1,i a_2),(ia_2,a_1)] is non-singular (d)none of these

Suppose a_1, a_2, are real numbers, with a_1!=0. If a_1, a_2,a_3, are in A.P., then (a) A=[(a_1,a_2,a_3),(a_4,a_5,a_6),(a_5,a_6,a_7)] is singular (where i=sqrt(-1) ) (b)The system of equations a_1x+a_2y+a_3z=0,a_4x+a_5y+a_6z=0,a_7x+a_8y+a_9z=0 has infinite number of solutions. (c) B=[(a_1,i a_2),(ia_2,a_1)] is non-singular (d)none of these

If a_r=(cos2rpi+isin2rpi)^((1)/(9)) , then the value of |{:(a_1,a_2,a_3),(a_4,a_5,a_6),(a_7,a_8,a_9):}| .

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 .

If a_1,a_2,a_3,5,4,a_6,a_7,a_8,a_9 are in H.P. , and D=|(a_1,a_2,a_3),(5,4,a_6),(a_7,a_8,a_9)| , then the value of [D] is (where [.] represents the greatest integer function)