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Matrices and Determinants question

2022 · 29 Jun · Shift 2 · Q42
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Matrices and Determinants question

2022 · 29 Jun · Shift 2 · Q42

JEE MainMathematicsMatrices and DeterminantsNumerical+4 / −1
Let M=[0−αα0]M = \left[ {\begin{matrix} 0 & { - \alpha } \\ \alpha & 0 \\ \end{matrix} } \right]M=[0α​−α0​], where α\alphaα is a non-zero real number an N=∑k=149M2kN = \sum\limits_{k = 1}^{49} {{M^{2k}}}N=k=1∑49​M2k. If (I−M2)N=−2I(I - {M^2})N = - 2I(I−M2)N=−2I, then the positive integral value of α\alphaα is ‾\underline{\hspace{2cm}}​.
Numerical answer
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