Let A = 1 1/51 0 1. If B = 1 2 -1 -1 A -1 -2 1 1, then the sum of… | JEE Main 2023 Mathematics PYQ

MCQMediumJEE Main 2023 · 12 April, Shift 1Algebra of Matrices

Let $A = \begin{bmatrix} 1 & \frac{1}{51}\\0 & 1 \end{bmatrix}$ . If $B = \begin{bmatrix} 1 & 2\\-1 & -1 \end{bmatrix} A \begin{bmatrix} -1 & -2\\1 & 1 \end{bmatrix}$ , then the sum of all the elements of the matrix $\sum_{n=1}^{50} B^n$ is equal to:

A
$100$
B
$50$
C
$75$
D
$125$

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