Suppose that a2 = 0 for some matrix a. prove that the only possible eigenvalues of a are then 0.

The eigenvector of A is not equal to zero, then we can say λ or λ = 0. Therefore,  the only possible eigenvalues of A are 0.

Step-by-step explanation:

If we assume that λ is the eigenvalue of the matrix A and the eigenvector of the matrix A is ⁻ˣ. Therefore:

For

we have:

⁻0 = [⁰₀⁰₀][⁻ˣ] = *[⁻ˣ] = Aλ[⁻ˣ] = λ[⁻ˣ]

In the expression above, ⁻ˣ is not equal to zero, then λ = 0 or  λ is = 0. This shows that the only possible eigenvalues of A are zero '0'

ok then what happened.