Find a matrix B such that B^3 = ((9,1),(-1,7)). B can have complex values.

Question

I have found the Jordan Normal form of the matrix ((9,1),(-1,7)) which is J = ((8,0)(1,8)). We have learnt that the 1's in the Normalform come under the main diagonal so that its a lower triangular matrix. I have also found the Jordan basis which are {(1,0)^t , (1,-1)^t}. How do I find a matrix B with this.

Answer 1

Hint: find $x$ so that $$\pmatrix{2 & 0\cr x & 2\cr}^3 =\pmatrix{8 & 0\cr 1 & 8\cr}$$