Consider an eigenvalue problem given by $\mathbf{A x}=\lambda_{\mathrm{i}} \mathbf{x}$. If $\lambda_{\mathrm{i}}$ represent the eigenvalues of the nonsingular square matrix $\mathbf{A}$, then what will be the eigenvalues of matrix $\mathbf{A}^{2}$ ?
(A) $\lambda_{\mathrm{i}}^{4}$
(B) $\lambda_{\mathrm{i}}^{2}$
(C) $\lambda_{\mathrm{i}}^{1 / 2}$
(D) $\lambda_{\mathrm{i}}^{1 / 4}$
Consider an eigenvalue problem given by $\mathbf{A x}=\lambda_{\mathrm{i}} \mathbf{x}$. If $\lambda_{\mathrm{i}}$ represent the eigenvalues of the nonsingular square matrix $\mathbf{A}$, then what will be the eigenvalues of matrix $\mathbf{A}^{2}$ ?
(A) $\lambda_{\mathrm{i}}^{4}$
(B) $\lambda_{\mathrm{i}}^{2}$
(C) $\lambda_{\mathrm{i}}^{1 / 2}$
(D) $\lambda_{\mathrm{i}}^{1 / 4}$