JEE Main 2019 · Mathematics · Matrices and Determinants · hard

For the matrix A=beginbmatrix1&2\\0&1endbmatrix, the total of all four entries of A^10 is

Single correct option

For the matrix

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

, the total of all four entries of

A^{10}

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Answer: (C) 22

By induction

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

(each multiplication adds 2 to the top-right entry). So

A^{10}=\begin{bmatrix}1&20\\0&1\end{bmatrix}

and the sum of entries is

1+20+0+1=22

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