Square/Standard vectors as vertices/Symmetry group/Matrices/Exercise

Let $Q$ be the square in ${ℝ}^2$ with the vertices $(1,0),(0,1),(-1,0),(0,-1)$.

a) Determine for every proper symmetry of this square the describing matrix with respect to the standard basis.

b) Determine for every improper symmetry of this square the describing matrix with respect to the standard basis.

c) Is the group of all proper and improper symmetries of this square commutative?

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