CSIR NET Mathematics 2022| Linear Algebra (4 OCTOBER)

Let A & B be two n × n matrices over a field F then

Let M be a real matrix which has 0, 1, and -1 as eigen values which of the following is  true of M?

If  then which of the following is/are true.

Let A be the n × n matrix whose main diagonal entries are zero and elsewhere 1

i.e., a_ii = 0, 1 ≤ i ≤ n & a_ij = 1, i ≠ j then what are eigenvalues of A

Let V be the set of all polynomials of degree ≤ 2. Define T: V → V by T(p(x)) = p (1) + p (2) x + p (0) x², p(x) ∈ V. Then the trace of the matrix representing T is