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Linear map equation and its solution

Consider the linear transformation T:RT:R2→RR2 defined by T(x,y)=(x,0)T(x, y)=(x, 0), where x,y∈Rx, y∈R. Then range of TT is
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Consider the linear transformation T:RT:R3→RR2 defined by T(x,y,z)=(x,y+z)T(x, y, z)=(x, y+z), where x,y,z∈Rx, y, z∈R. Then range of TT is
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Consider the linear transformation T:RT:R2→RR2 defined by T(x,y)=(x,−y)T(x, y)=(x, -y), where x,y∈Rx, y∈R. Then
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Consider the linear transformation T:RT:R3→RR2 defined by T(x,y,z)=(x+y+z,0)T(x, y, z)=(x+y+z, 0), where x,y,z∈Rx, y, z∈R. Then
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Consider the map T:RT:R2→RR3 such that T(1,3)=(1,0,0)T(1, 3)=(1, 0, 0), T(2,6)=(2,0,0)T(2, 6)=(2, 0, 0), T(1,1)=(0,1,0)T(1, 1)=(0, 1, 0) and T(2,4)=(1,1,0)T(2, 4)=(1, 1, 0). Then TT is
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Consider the map T:RT:R2→RR2 and S:RR2→RR2 such that T(2,1)=(1,1),T(1,2)=(1,1),S(4,2)=(3,3)T(2, 1)=(1, 1), T(1, 2)=(1, 1), S(4, 2)=(3, 3) and S(8,4)=(5,6)S(8, 4)=(5, 6). Let the statements AA and BB be as given below: AA: TT is one-to-one. B:SB: S is not linear. Then which of following holds
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