SOLUTION: Let T(x,y,z) = (y,z,0). Prove that T^3 must be a zero transformation (T^3=ToToT)

SOLUTION: Let T(x,y,z) = (y,z,0). Prove that T^3 must be a zero transformation (T^3=ToToT)

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Question 372421: Let T(x,y,z) = (y,z,0). Prove that T^3 must be a zero transformation (T^3=ToToT)
Answer by user_dude2008(1862) (Show Source): You can put this solution on YOUR website!
T(a, b, c) = (b, c, 0)

(T o T)(a, b, c) = T(b, c, 0) = (c, 0, 0)

(T o T o T)(a, b, c) = T(b, c, 0) = T(c, 0, 0) = (0,0,0)

Therefore, (T o T o T)(a, b, c) = (0,0,0)
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