Mathematics · 2016
JEE Main · 10 April 2016, Shift 1 · Q64
Let A be a 3 × 3 matrix such that A^2-5 A +7 I = O. Statement - I: A^-1=1/7(5 I - A ). Statement - II: The polynomial A^3-2 A^2-3 A + I can be…
Let A be a $\displaystyle 3 \times 3$ matrix such that $\displaystyle \mathrm{A}^2-5 \mathrm{~A}+7 \mathrm{I}=\mathrm{O}$.Statement - I : $\displaystyle \mathrm{A}^{-1}=\frac{1}{7}(5 \mathrm{I}-\mathrm{A})$.
Statement - II : The polynomial $\displaystyle \mathrm{A}^3-2 \mathrm{~A}^2-3 \mathrm{~A}+\mathrm{I}$ can be reduced to $\displaystyle 5$(A - 4I).
Then :
Official answer
(3)
Both the statements are true.
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JEE Main 2016 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.