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NDA 2017

Exam: NDA
Year: 2017
Subject: Mathematics
Chapter: Matrices

NDA 2017 · Mathematics · Matrices

If A=[ array ll 0 & 1 1 & 0 array ] , then the value of A^4 is

If

A=\left[

\begin{array}{ll}0 & 1 \\ 1 & 0\end{array}

\right]

, then the value of

A^4

is

Options

A $\left[$ $\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}$ $\right]$
B $\left[$ $\begin{array}{ll}1 & 1 \\ 0 & 0\end{array}$ $\right]$
C $\left[$ $\begin{array}{ll}0 & 0 \\ 1 & 1\end{array}$ $\right]$
D $\left[$ $\begin{array}{ll}0 & 1 \\ 1 & 0\end{array}$ $\right]$

Correct answer

A. $\left[$ $\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}$ $\right]$

Step-by-step solution

\begin{aligned} & A=\left[\begin{array}{ll}0 & 1 \\ 1 & 0\end{array}\right] \\ & A^4=A^2 \cdot A^2 \\ & = \left[\begin{array}{ll}0 & 1 \\ 1 & 0\end{array}\right]\left[\begin{array}{ll}0 & 1 \\ 1 & 0\end{array}\right] \cdot \left[\begin{array}{ll}0 & 1 \\ 1 & 0\end{array}\right]\left[\begin{array}{ll}0 & 1 \\ 1 & 0\end{array}\right] \\ & =\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right] \cdot\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right] \\ & =\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]\end{aligned}

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