Let A=I_2-2 M M^T, where M is a real matrix of order 2 × 1 such that the relation M^T M = I_1 holds. If λ is a real number such that the relation A X…

Let $\displaystyle A=I_2-2 M M^T$, where $\displaystyle M$ is a real matrix of order $\displaystyle 2 \times 1$ such that the relation $\displaystyle \mathrm{M}^{\mathrm{T}} \mathrm{M}=\mathrm{I}_1$ holds. If $\displaystyle \lambda$ is a real number such that the relation $\displaystyle \mathrm{A} \mathrm{X}=\lambda \mathrm{X}$ holds for some non-zero real matrix $\displaystyle X$ of order $\displaystyle 2 \times 1$, then the sum of squares of all possible values of $\displaystyle \lambda$ is equal to $\displaystyle \_\_\_\_$.