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Home  >>  JEEMAIN and NEET  >>  Mathematics  >>  Class12  >>  Matrices

If $A=\begin{bmatrix}1&2&2\\2&1&2\\2&2&1\end{bmatrix}$ then $A^2-4A$ is equal to

$(a)\;2I_3\qquad(b)\;3I_3\qquad(c)\;4I_3\qquad(d)\;5I_3$

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1 Answer

$A=\begin{bmatrix}1&2&2\\2&1&2\\2&2&1\end{bmatrix}$
$A^2=\begin{bmatrix}1&2&2\\2&1&2\\2&2&1\end{bmatrix}\begin{bmatrix}1&2&2\\2&1&2\\2&2&1\end{bmatrix}$
$\;\;\;\;=\begin{bmatrix}9&8&8\\8&9&8\\8&8&9\end{bmatrix}$
$A^2-4A=\begin{bmatrix}9&8&8\\8&9&8\\8&8&9\end{bmatrix}-\begin{bmatrix}4&8&8\\8&4&8\\8&8&4\end{bmatrix}$
$\;\;\;\qquad=\begin{bmatrix}5&0&0\\0&5&0\\0&0&5\end{bmatrix}$
$\;\;\;\qquad=5I_3$
Hence (d) is the correct answer.
answered Nov 22, 2013 by sreemathi.v
 

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