Let the matrix A = 1 0 0 1 0 1 0 1 0 satisfy Aⁿ = Aⁿ⁻² + A² - I f… | JEE Main 2025 Mathematics PYQ

MCQMediumJEE Main 2025 · 4 April, Shift 2Algebra of Matrices

Let the matrix $A = \begin{pmatrix} 1 & 0 & 0 \\ 1 & 0 & 1 \\ 0 & 1 & 0 \end{pmatrix}$ satisfy $A^n = A^{n-2} + A^2 - I$ for $n \geq 3$ . Then the sum of all the elements of $A^{50}$ is:

A
$53$
B
$52$
C
$39$
D
$44$

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