Question

If $A=\left[\begin{array}{cc}4& 2\\ -1& 1\end{array}\right]$ and I is the identity matrix of order 2, then (A - 2I)(A - 3I) =

• A. $I$
• B. $0$
• C. $\left[\begin{array}{cc}1& 0\\ 0& 0\end{array}\right]$
• D. $\left[\begin{array}{cc}0& 0\\ 0& 1\end{array}\right]$

Answer 1

The correct option is B $0$

$(A-2I)(A-3I)=\left[\begin{array}{cc}2& 2\\ -1& -1\end{array}\right]\left[\begin{array}{cc}1& 2\\ -1& -2\end{array}\right]=\left[\begin{array}{cc}0& 0\\ 0& 0\end{array}\right]=0$