QJEEM24Ma005f: JEE Main 2024 Mathematics - Class 12 JEEM24Ma005f Solution: Let , where is a real matrix of order such that the relation…

Let $A=I_2-2 M M^T$ , where $M$ is a real matrix of order $2 \times 1$ such that the relation $M^T M=I_1$ holds. If $\lambda$ is a real number such that the relation $A X=\lambda X$ holds for some non-zero real matrix $X$ of order $2 \times 1$ , then the sum of squares of all possible values of $\lambda$ is equal to __________.