List of top Mathematics Questions on Eigenvalues asked in IIT JAM MA

Let \( \alpha, \beta, \gamma, \delta \) be the eigenvalues of the matrix

\[ \begin{pmatrix} 0 & 0 & 0 & 0 \\ 1 & 0 & -2 & 0 \\ 0 & 1 & 1 & 0 \\ 0 & 0 & 2 & 0 \end{pmatrix} \] Then \( \alpha^2 + \beta^2 + \gamma^2 + \delta^2 = \) ..........

Let \( M \) be an \( n \times n \) matrix with real entries such that \( M^3 = I \). Suppose that \( Mv \neq v \) for any non-zero vector \( v \). Then which of the following statements is/are TRUE?