prove or disprove let V be a vector space with dim V2 Soluti

prove or disprove

let V be a vector space with dim V=2 .

Solution

let T *.T = identity = 0 = T(0)

when T is aLinear transformation then T(0) = 0 \' = id element of the codomain

here codomain = V

hence 0 \' = 0

T(0)=0 => T * T (x) = T(0) =0 => T(x) = 0

valid only for the elements in the kernelm of the Linear transformation T not all elements of V

hence there does nt exist a LT such tat : T*T = id