(a) Let O: Rn → Rm be the matrix transformation defined by 0(u) = Ou, where O is the m × n zero matrix. Show that O(u) = 0 for all u in Rn.
(b) Let I: Rn → Rn be the matrix transformation defined by I(u) = Inu, where In is the identity matrix. (See Section 1.5.) Show that I(u) = u for all u in Rn.