यदि A= [ ll 1 & a 0 & 1 ] हो, तो A^4 बराबर है-

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यदि $A=\left[\begin{array}{ll}1 & a \\ 0 & 1\end{array}\right]$ हो, तो $A^4$ बराबर है$-$

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Answer

$\begin{array}{l} A ^2= A \cdot A =\left[\begin{array}{ll}1 & a \\ 0 & 1\end{array}\right]\left[\begin{array}{ll}1 & a \\ 0 & 1\end{array}\right]\end{array} $
$A ^2=\left[\begin{array}{cc}1 & 2 a \\ 0 & 1\end{array}\right]$
$A ^4= A ^2 A^2=\left[\begin{array}{cc}1 & 2 a \\ 0 & 1\end{array}\right]\left[\begin{array}{cc}1 & 2 a \\ 0 & 1\end{array}\right]$
$=\left[\begin{array}{cc}1+0 & 2 a+2 a \\ 0+0 & 0+1\end{array}\right]$
$=\left[\begin{array}{cc}1 & 4 a \\ 0 & 1\end{array}\right]$

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