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Which one of the following statements is NOT true for a square matrix $A$?

  1.  If  $A$  is upper triangular, the eigenvalues of $A$ are the diagonal elements of it
  2. If  $A$  is real symmetric, the eigenvalues of $A$ are always real and positive
  3. If  $A$  is real, the eigenvalues of $A$  and $A ^T\:\text{(A transpose)}$ are always  the same
  4. If all the principal minor of $A$ are positive, all the eigenvalues of $A$ are  also positive
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