Question

If $A=\left[\begin{array}{ccc}1& 4& 4\\ 4& 1& 4\\ 4& 4& 1\end{array}\right]$, then $A^2-6A=$

• A. $27I_3$
• B. $5I_3$
• C. $20I_3$
• D. $30I_3$

Answer 1

The correct option is A $27I_3$

$A^2=\left[\begin{array}{ccc}1& 4& 4\\ 4& 1& 4\\ 4& 4& 1\end{array}\right]\times \left[\begin{array}{ccc}1& 4& 4\\ 4& 1& 4\\ 4& 4& 1\end{array}\right]$

$=\left[\begin{array}{ccc}33& 24& 24\\ 24& 33& 24\\ 24& 24& 33\end{array}\right]$

$A^2-6A=\left[\begin{array}{ccc}33-6& 24-24& 24-24\\ 24-24& 33-6& 24-24\\ 24-24& 24-24& 33-6\end{array}\right]$

$\therefore A^2-6A=27I_3$