If `a^2 + a + 1 = 0` , then find `a^3 - 1^3`

If x^(2)+3x+1=0 then find x^(3)+(1)/(x^(3)),x^(4)+(1)/(x^(4)),x^(2)-(1)/(x^(2)),x^(2)+(1)/(x^(2))

If x^(2)-2x+1=0 then find (i)x^(3)+(1)/(x^(3))(ii)x^(4)+(1)/(x^(4))(iii)x^(2)-(1)/(x^(2))(iv)x^(2)+(1)/(x^(2))

If Delta=|(1,a, a^2), (a, a^2, 1),(a^2, 1,a)|=-4 then find the value of |(a^3-1, 0,a-a^4), (0,a-a^4, a^3-1), (a-a^4,a^3-1, 0)|.

If A = a [{:(-1, 0), (-1, 2):}]"nd B "= [{:(3, 2), (-1, 0):}], " then find "B^(-1), A^(-1).

If A = [(0,1),(2,3),(1,-1)]and B = [(1,2,1),(2,1,0)] , then find (AB)^(-1)

If A=[[1,2,-3] , [5,0,2] , [1,-1,1]] and B=[[3,-1,2] , [4,2,5] , [2,0,3]] then find matrix C such that A+2C=B

(1+2/3+6/3^2+10/3^3+. . . + oo)^(log_(0.25)(1/3+1/3^2+1/3^3+. . . +oo)) is equal L and then find L^2

If Delta=|{:(1,a,a^(2)),(a,a^(2),1),(a^(2),1,a):}|=-4 , then find the value of : |{:(a^(3)-1,0,a-a^(4)),(0,a-a^(4),a^(3)-1),(a-a^(4),a^(3)-1,0):}|