JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
If \(A = \left[ {\begin{array}{*{20}{c}}
{ - 4}&{ - 1}\\
3&1
\end{array}} \right]\) , then the determinant of the matrix \(\left( {{A^{2016}} - 2{A^{2015}} - {A^{2014}}} \right)\) is
- A \(-175\)
- B \(2014\)
- C \(2016\)
- D \(-25\)
Answer & Solution
Correct Answer
(D) \(-25\)
Step-by-step Solution
Detailed explanation
\(A = \left[ {\begin{array}{*{20}{c}} { - 4}&{ - 1}\\ 3&1 \end{array}} \right]\) \( \Rightarrow {A^2} = \left[ {\begin{array}{*{20}{c}} { - 4}&{ - 1}\\ 3&1 \end{array}} \right]\left[ {\begin{array}{*{20}{c}} { - 4}&{ - 1}\\ 3&1 \end{array}} \right]\)…
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