Consider the square matrix , , where the generic element is given by

Which of the following statements is true?

Question

Consider the square matrix   ,   , where the generic element is given by 
  
 Which of the following statements is true?

Answer

The product of all eigenvalues of    is equal to the determinant of    and    has two positive eigenvalues and three negative ones.

Answer

The sum of all eigenvalues of    is equal to the trace of    and    is negative.

Answer

The product of all eigenvalues of    is equal to the determinant of    and    has exactly one positive eigenvalue and four negative ones.

Answer

The product of all eigenvalues of    is equal to the trace of    and    has exactly one positive eigenvalue and four negative ones.

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