The cyclic group of order 4 has members (left{mathbf{E}, mathbf{A}, mathbf{B}=mathbf{A}^{2}, mathbf{C}=mathbf{A}^{3}ight}), and its product table is.

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The cyclic group of order 4 has members \(\left\{\mathbf{E}, \mathbf{A}, \mathbf{B}=\mathbf{A}^{2}, \mathbf{C}=\mathbf{A}^{3}ight\}\), and its product table is.

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Write the regular representation of group member \(\mathbf{A}\).

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