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  4. If B is a 3 × 3 matrix such that B2 = 0, then det. [(I + B)50 - 50B] is equal to:

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Q. If B is a $3 \times 3$ matrix such that $B^2 = 0$, then det. $[(I + B)^{50} - 50B]$ is equal to:

JEE MainJEE Main 2014Determinants

Solution:

$\left[(1+ B )^{50}-50 B \right]=1+50 B +\frac{50.49}{\lfloor 2} B ^{2}+\ldots \ldots . .-50 B$
$=1+ B ^{2}\{---------\}= 1 + 0 \{----------\}=1$