Let P be a fixed (but unknown) 3 x 2 matrix. Define a new subset Tp CM Tp = {A EM | AP = PA} i. Show that Tp is closed under addition ii. Show that Tp is closed under scalar multiplication iii. Determine if Tp is a subspace of M. If so, find a basis and the dimension of the subspace. If not, provide a reason why it fails to be a subspace.

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