MathsJEE Main 28 Jan 2026, Shift 2·Q25·Numerical·Moderate

Matrices & Determinants · Powers of a nilpotent matrix

Let

A = \begin{bmatrix} 3 & -4\\ 1 & -1\end{bmatrix}

and

B

be two matrices such that

A^{100} = 100B + I

. Then the sum of all the elements of

B^{100}

is .

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