Question

If the matrix $A=\left[\begin{array}{cc}2& 5\\ 1& 3\end{array}\right]$ , then the value of $\frac{|A^{100}+A^{98}|}{|A^{20}+A^{18}|}$ is equal to

• A. $0$
• B. $1$
• C. $2$
• D. $3$

Answer 1

Answer: (B)

$\left|A\right|=\left|\begin{array}{cc}2& 5\\ 1& 3\end{array}\right|=6-5=1$
$\frac{|A^{100}+A^{98}|}{|A^{20}+A^{18}|}=\frac{|A^{98}||A^2+I|}{|A^{18}||A^2+I|}={\left|A\right|}^{80}=1$