Answer:
The eigenvector of A is not equal to zero, then we can say λ[tex]^{2}[/tex] 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 [tex]A^{2} = 0[/tex]
we have:
⁻0 = [⁰₀⁰₀][⁻ˣ] = [tex]A^{2}[/tex]*[⁻ˣ] = Aλ[⁻ˣ] = λ[tex]^{2}[/tex][⁻ˣ]
In the expression above, ⁻ˣ is not equal to zero, then λ[tex]^{2}[/tex] = 0 or λ is = 0. This shows that the only possible eigenvalues of A are zero '0'
