JEE Main 2005Annual, Paper 1MathematicsMediumMathematical Induction3× since 2002If A=[1011]A = \left[ {\matrix{ 1 & 0 \cr 1 & 1 \cr } } \right]A=[1101] and I=[1001],I = \left[ {\matrix{ 1 & 0 \cr 0 & 1 \cr } } \right],I=[1001], then which one of the following holds for all n≥1,n \ge 1,n≥1, by the principle of mathematical induction?AOption A. An=nA−(n−1)I{A^n} = nA - \left( {n - 1} \right){\rm I}An=nA−(n−1)IBOption B. An=2n−1A−(n−1)I{A^n} = {2^{n - 1}}A - \left( {n - 1} \right){\rm I}An=2n−1A−(n−1)ICOption C. An=nA+(n−1)I{A^n} = nA + \left( {n - 1} \right){\rm I}An=nA+(n−1)IDOption D. An=2n−1A+(n−1)I{A^n} = {2^{n - 1}}A + \left( {n - 1} \right){\rm I}An=2n−1A+(n−1)ICheckSkip · show solution
