16. Show that o(x) = 3x from Z12 to Z12 is a homomorphism. Let a, b E x 3(a + b) = 3a + 3b = p(a) + p(b) 17. Find the Ker o from Question 16. P(8) = 3 * 8 = 24 = 0 P(0) = 3 * 0 = 0 P(4) = 3 * 4 = 12 =...

I need help with # 18 attached for abstract algebra plz. can u list steps clearly so I know how do do these inverses

Extracted text: 16. Show that o(x) = 3x from Z12 to Z12 is a homomorphism. Let a, b E x 3(a + b) = 3a + 3b = p(a) + p(b) 17. Find the Ker o from Question 16. P(8) = 3 * 8 = 24 = 0 P(0) = 3 * 0 = 0 P(4) = 3 * 4 = 12 = 0 p(1) = 3 * 1 = 3 p(9) = 3 * 9 = 27 = 3 p(5) = 3 * 5 = 15 p(10) = 3 * 10 = 30 = 6 p(2) = 3 * 2 = 6 p(6) = 3 * 6 = 18 p(11) = 3 * 11 = 33 = 9 p(2) = 3 * 3 = 9 p(7) = 3 * 7 = 21 %3D Kernal ={[0],[4],[8]) 18. Find o(5) from Question 16.