Linear Algebra - Eigenvalues

The matrix $\begin{bmatrix} 1 & a \\ 8 & 3 \end{bmatrix}$ (where $a > 0$) has a negative eigenvalue if $a$ is greater than

Consider an n×n matrix A and a non-zero n × 1 vector p. Their product Ap = α²p, where α ∈ R and α ∉ {−1, 0, 1}. Based on the given information, the eigen value of A² is:

Consider the matrix P = $\begin{bmatrix} 1 & 1 & 0 \\ 0 & 1 & 1 \\ 0 & 0 & 1 \end{bmatrix}$. The number of distinct eigenvalues of P is

The product of eigenvalues of the matrix P is P = [[2, 0, 1], [4, -3, 3], [0, 2, -1]]

The determinant of a 2×2 matrix is 50. If one eigenvalue of the matrix is 10, the other eigenvalue is