There are only two distinct groups of order 4. One of them is the group for rotations

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There are only two distinct groups of order 4. One of them is the group for rotations of a square, Problem 8 . Here is the product table of the other.

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Show that \(\{\mathbf{E}, \mathbf{K}, \mathbf{L}, \mathbf{M}\}\) indeed form a group. Is it an Abelian group? Is it a cyclic group? Explain.

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