(a) Consider the group D4 = (x, y; x¹, y², yxyx). Check that the map p: D4 → GL3(R), defined by 0 1 0 0 0 0 1 0 0 p(x): =-1 0 1 p(y) = 0 -1 0 [001] extends to a representation of D4. Also determine the character of p.

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