For \(A=\left[\begin{array}{ll}2 & 3\\ 1& 2\end{array}\right]\) which of the following is true:
Answer & explanation
Correct answer: option 3
$A=\left[\begin{array}{ll}2 & 3\\ 1& 2\end{array}\right]$
$⇒A^2=\left[\begin{array}{ll}2 & 3\\ 1& 2\end{array}\right]\left[\begin{array}{ll}2 & 3\\ 1& 2\end{array}\right]=\left[\begin{array}{ll}7 & 12\\ 4& 7\end{array}\right]$
$⇒A^2-4A+I=\left[\begin{array}{ll}7 & 12\\ 4& 7\end{array}\right]-4\left[\begin{array}{ll}2 & 3\\ 1& 2\end{array}\right]-\left[\begin{array}{ll}1 & 0\\ 0& 1\end{array}\right]$
$=0$