(1) {[cos2pi/7   -sin2pi/7]

[sin2pi/7     cos2pi/7]}ki power k = I(identity matrix)

then find the least value of k.

ans=7.

Let k=2pi/7 and the matrix be A then the matrix becomes

A=[cosk   -sink   and A²=[cos2k  -sin2k    and so on

     sink    cosk]                sin2k    cos2k]

Therefore,A^p=I iff [cospk  -sinpk   =[1  0   iff cospk=1 and sinpk=0

                             sinpk    cospk]    0  1] 

The min value of p satisfying these conditions is p=7