Question

# If (a) $A=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$, if n is an even natural number (b) $A=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$, if n is an odd natural number (c) (d) none of these

Solution

## Disclaimer: In all option, the power of A (i.e. n is missing) (a) ${A}^{n}=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$, if n is an even natural number $A=\left[\begin{array}{cc}2& -1\\ 3& -2\end{array}\right]\phantom{\rule{0ex}{0ex}}{A}^{2}=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]\phantom{\rule{0ex}{0ex}}⇒A×A=I\phantom{\rule{0ex}{0ex}}⇒{A}^{-1}=A\phantom{\rule{0ex}{0ex}}$ Generally, MathematicsRD Sharma XII Vol 1 (2015)Standard XII

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