1. Suppose A is 5 5 matrix with the following properrties:

(i) A has integer entries,

(ii) A is not digonalizable over C ( Complex nummber)

(iii) the minimum and charteristic polynomial of A are different,

(iv) 1 and 2i are two (but not necessarily all) eigenvalues of A.

Determine the minimum polynomial, the characteristic polynomial, and the Jordan form of A.