In this table representing the binary operation ⊗:

\(

\begin{array}{cccc}

\begin{array}{c}

\text{⊗} \\

\end{array} & \begin{array}{c}

k \\

\end{array} & \begin{array}{c}

l \\

\end{array} & \begin{array}{c}

m \\

\end{array} \\

k & l & m & k \\

l & m & k & l \\

m & k & l & m \\

\end{array}

\)

We're looking for an identity element \(e\) such that when we use the operation ⊗ to combine it with any other element (k, l, or m), we get back that other element unchanged.

In other words, for any element \(x\) in the set {k, l, m}, we want \(x ⊗ e = x\).

Let's go through each element and see if we can find such an identity element:

1. For k:

- \(k ⊗ k = l\)

- \(k ⊗ l = m\)

- \(k ⊗ m = k\)

None of these results in \(k\), so \(k\) is not the identity element.

2. For l:

- \(l ⊗ k = m\)

- \(l ⊗ l = k\)

- \(l ⊗ m = l\)

None of these results in \(l\), so \(l\) is not the identity element.

3. For m:

- \(m ⊗ k = k\)

- \(m ⊗ l = l\)

- \(m ⊗ m = m\)

In all cases, using the element \(m\) with the operation ⊗ gives back the same element \(m\), which is the definition of an identity element.

So, the element \(m\) is the only one that acts as an identity element for this operation, and that's why the correct answer is m