f(z)=[[1,2,3],[3,2,1],[2,3,1]]," So prove that "AI_(3)^(2)=I_(3)

If A=[[3,3,52,3,45,2,3]]. Prove that AI_(3)=I_(3)A

If A=[{:(0,1),(0,0):}]andI=[{:(1,0),(0,1):}] then prove that (aI+bA)^(3)=a^(3)I+3a^(2)bA .

If z_(r)=cos((pi)/(3^(r)))+i sin((pi)/(3^(r))),r=1,2,3 prove that z_(1)z_(2)z_(3)z_(oo)=i

The identity matrix I_(2)={:[(1,0),(0,1)]:} . If A={:[(2,-3),(5,1)]:} , evaluate AI_(2)=I_(2)A=A

If z_(1)=iz_(2) and z_(1)-z_(3)=i(z_(3)-z_(2)), then prove that |z_(3)|=sqrt(2)|z_(1)|

For z_(1)=""^(6)sqrt((1-i)//(1+isqrt(3))),z_(2)=""^(6)sqrt((1-i)//(sqrt(3)+i)) , z_(3)= ""^(6)sqrt((1+i) //(sqrt(3)-i)) , prove that |z_(1)|=|z_(2)|=|z_(3)|

For z_(1)=""^(6)sqrt((1-i)//(1+isqrt(3))),z_(2)=""^(6)sqrt((1-i)//(sqrt(3)+i)) , z_(3)= ""^(6)sqrt((1+i) //(sqrt(3)-i)) , prove that |z_(1)|=|z_(2)|=|z_(3)|

Let z_(1),z_(2) and z_(3) be complex numbers such that |z_(1)|=|z_(2)|=|z_(3)|=1 then prove that |z_(1)+z_(2)+z_(3)|=|z_(1)z_(2)+z_(2)z_(3)+z_(3)z_(1)|

If z_(1)=-3i,z_(2)=3+4i and z_(3)=2-3i , verify that z_(1)(z_(2)+z_(3))=z_(1)z_(2)+z_(1)z_(3) .

If z = 2 + i, prove that z^(3) + 3z^(2) - 9z + 8 = (1 + 14i) .