If A = [ array ll 1 & 0 1 & 1 array ] and I = [ array ll 1 & 0 0 & 1 array ] , then which…
Mathematics · JEE Main · NTA Exams — Matrices and Determinants
If A = \(\left[\begin{array}{ll}
1 & 0 \\
1 & 1
\end{array}\right] \text { and } \mathrm{I}=\left[\begin{array}{ll}
1 & 0 \\
0 & 1
\end{array}\right] \text {, }\)then which one of the following holds for all n ³ 1, by the principle of mathematical induction ?
- An = 2n–1 A – (n – 1) I
- An = nA – (n – 1) I
- An = 2n–1 A + (n – 1) I
- An = nA + (n – 1) I
Answer
(B) A n = nA – (n – 1) I
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