Question 1090124: Dear Tutor,
Let A = {2,4,16}, and f={(2,4), (4,16), (16,2)} be a relation on A. Which one of the following is f^2?
a) {(4,4), (16,16), (256,2)}
b) {(2,16), (4,256), (16,4)}
c) {(2,4), (4,16), (16,2)}
d) {(4,16), (16,28), (256,4)}
e) {(2,4), (2,16), (4,16), (4,256), (16,2), (16,4)}
The correct answer is under c) {(2,4), (4,16), (16,2)}
This is what I have so far:
I was trying to solve the problem with the use of matrix, and this is the matrix of the f:
0 1 0
0 0 1
1 0 0
Then I multiplied it by itself, and got:
0 0 1
1 0 0
0 1 0
Then I transformed the matrix back to the set of pairs and got these pairs: {(2,16), (4,2), (16,4)}
What am I doing wrong?
Please explain it to me so that I can learn from it.
Thank you for your help.
Answer by MathLover1(20850)   (Show Source):
You can put this solution on YOUR website!
if A = {2,4,16}, and f={(2,4), (4,16), (16,2)} be a relation on A, both have numbers from A
only c) {(2,4), (4,16), (16,2)} is a set with ordered pairs that have  , , and 
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