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Mathematics · 2022

JEE Main · 29 June 2022, Shift 1 · Q10

Let A =[ a_i j] be a square matrix of order 3 such that a_i j=2^j-i, for all i, j=1,2,3. Then, the matrix A^2+ A^3+…+ A^10 is equal to:

Let $\displaystyle \mathrm{A}=\left[\mathrm{a}_{i j}\right]$ be a square matrix of order $\displaystyle 3$ such that $\displaystyle \mathrm{a}_{i j}=2^{j-i}$, for all $\displaystyle i, j=1,2,3$. Then, the matrix $\displaystyle \mathrm{A}^2+\mathrm{A}^3+\ldots+\mathrm{A}^{10}$ is equal to :
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JEE Main 2022 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.