Question: Consider the laws of exponents Ar As = Ar+s and (Ar)s = Ars. (a) Show that if A is any square matrix, then these laws

Consider the laws of exponents Ar As = Ar+s and (Ar)s = Ars.
(a) Show that if A is any square matrix, then these laws are valid for all nonnegative integer values of r and s.
(b) Show that if A is invertible, then these laws hold for all negative integer values of r and s.

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