Question

If $A=\left[\begin{array}{cc}1& 2\\ 3& 5\end{array}\right]$ then the value of the determinant $\left|A^{2018}-5A^{2017}\right|$ is equal to

• A. -6
• B. -4
• C. 4
• D. 6

Answer 1

Answer: (D)

$\Theta |A|=-1$
$\therefore \left|A^{2018}-5A^{2017}\right|=|A{|}^{2017}|A-5I|$
$=(-1{)}^{2017}\left|\left[\begin{array}{cc}-4& 2\\ 3& 0\end{array}\right]\right|=(-1)(-6)=6$