Let M = bmatrix 0 & - & 0 bmatrix , where is a non-zero real number and N = _ k=1 ^ 49 M^ 2k . If (I - M^ 2 )N = −2I, then the positive integral value of is _____.

JEE Main 2022 Mathematics question

Let M = , where is a non-zero real number and . If = −2I, then the positive integral value of is .

Answer: 1

. So + … + + … ) I, a geometric series with 49 terms, first term and ratio , so $N =

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Question ID VK-035254