Question: Let K be a vector space over Z3 with basis {1, t}, so K = {a + bt | a, b in Z3}. It is

Let K be a vector space over Z3 with basis {1, t}, so K = {a + bt | a, b in Z3}. It is known that K becomes a field of nine elements if we define t2 = -1 in Z3. In each case find the inverse of the element x of K:
x = 1 + t.

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