Let the matrix A= 1 0 0 1 0 1 0 1 0 satisfy Aⁿ = Aⁿ⁻² + A² - I for n≥3. Then the sum of all the elements of A⁵⁰ is:

Matrices and Determinants: JEE Main 2025 Mathematics question

JEE Main 2025 · April, Unspecified (session-level dataset) · Q111

JEE Main 2025April, Unspecified (session-level dataset)MathematicsMediumMatrices and Determinants245× since 2002

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\ge3

. Then the sum of all the elements of

A^{50}

is:

JEE Main 2025 · April, Unspecified (session-level dataset) · Q111

JEE Main 2025April, Unspecified (session-level dataset)MathematicsMediumMatrices and Determinants245× since 2002

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\ge3

. Then the sum of all the elements of

A^{50}

is: