JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
If \(B\) is a \(3 \times 3\) matrix such that \(B^2 = 0\), then det. \([( I+ B)^{50} -50B]\) is equal to
- A \(1\)
- B \(2\)
- C \(3\)
- D \(50\)
Answer & Solution
Correct Answer
(A) \(1\)
Step-by-step Solution
Detailed explanation
det \(\left[ {{{\left( {I + B} \right)}^{50}} - 50B} \right]\) \(=\) det \([ {\,^{50}}{C_0}I + {\,^{50}}{C_1}B + {\,^{50}}{C_2}{B^2} + {\,^{50}}{C_3}{B^3} + ... +\) \( {\,^{50}}{C_{50}}{B^{50}}{B^{50}} - 50B]\) {All terms having \({B^n},2 \le n \le 50\) will be zero because…
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