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Questions  >>  JEEMAIN and NEET  >>  Mathematics  >>  Class12  >>  Matrices
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Q)

If $A=\begin{bmatrix}3&3&3\\3&3&3\\3&3&3\end{bmatrix}$ then $A^4$ is equal to

$(a)\;27A\qquad(b)\;81A\qquad(c)\;243A\qquad(d)\;729A$

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A)
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Given :
$A=\begin{bmatrix}3&3&3\\3&3&3\\3&3&3\end{bmatrix}$
$A=3\begin{bmatrix}1&1&1\\1&1&1\\1&1&1\end{bmatrix}$
$A^2=3\begin{bmatrix}1&1&1\\1&1&1\\1&1&1\end{bmatrix}3\begin{bmatrix}1&1&1\\1&1&1\\1&1&1\end{bmatrix}$
$\quad=9\begin{bmatrix}3&3&3\\3&3&3\\3&3&3\end{bmatrix}$
$A^4=A^2.A^2$
$\;\;\;\;\;=9A.9A$
$\;\;\;\;\;=81A^2$
$\;\;\;\;=81.9A$
$\;\;\;\;=729A$
Hence (d) is the correct answer.
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