JEE Main 2021 · Mathematics · Matrices and Determinants · easy

The sum of all the entries of A^25 is

Single correct option

Let

A=\begin{bmatrix}1&2\\0&1\end{bmatrix}

. The sum of all the entries of

A^{25}

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Answer: (C) $52$

By induction

A^n=\begin{bmatrix}1&2n\\0&1\end{bmatrix}

, since multiplying by

A

adds

2

to the upper-right entry. So

A^{25}=\begin{bmatrix}1&50\\0&1\end{bmatrix}

and the entry sum is

1+50+0+1=52

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