Here is a sample proof that contains an error. Explain why the proof is not correct.
Theorem: If $a \mid b$ and $b \mid c$, then $a \mid c$.
Proof: Since $a \mid b , b = a k$.
Since $b \mid c , c = b k$.
Therefore $c = b k = ( a k ) k = a k ^ { 2 }$.
Therefore $a \mid c$.

Question

Here is a sample proof that contains an error. Explain why the proof is not correct. 
Theorem: If $a \mid b$ and $b \mid c$, then $a \mid c$.
Proof: Since $a \mid b , b = a k$.
Since $b \mid c , c = b k$.
Therefore $c = b k = ( a k ) k = a k ^ { 2 }$.
Therefore $a \mid c$.

Quizplus · Accepted Answer

The Answer of Here is a sample proof that contains an error. Explain why the proof is not correct. 
Theorem: If $a \mid b$ and $b \mid c$, then $a \mid c$.
Proof: Since $a \mid b , b = a k$.
Since $b \mid c , c = b k$.
Therefore $c = b k = ( a k ) k = a k ^ { 2 }$.
Therefore $a \mid c$.

Here Is a Sample Proof That Contains an Error a∣ba \mid ba∣b

Here Is a Sample Proof That Contains an Error $a \mid b$