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JEE Main 2014 · 9 Apr · Shift 1, Mathematics question 66

If B is a 3×33\times3 matrix such that B2=0B^2=0, then det⁡[(I+B)50−50B]\det\left[(I+B)^{50}-50B\right] is equal to :

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Answer and worked solution

Official answer: A

With B2=0B^2=0, the binomial expansion stops: (I+B)50=I+50B(I+B)^{50}=I+50B. So the matrix is II, and its determinant is 1.

Topics:Matrix algebraDeterminants and properties
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