# A=begin{bmatrix}5 & 1 1 & 1 end{bmatrix} B=begin{bmatrix}3 & 5 1 & 3 end{bmatrix} Similar or not similar?

$A=\left[\begin{array}{cc}5& 1\\ 1& 1\end{array}\right]$
$B=\left[\begin{array}{cc}3& 5\\ 1& 3\end{array}\right]$
Similar or not similar?
You can still ask an expert for help

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

Jayden-James Duffy
Step 1
Given matrices, $A=\left[\begin{array}{cc}5& 1\\ 1& 1\end{array}\right]$ and $B=\left[\begin{array}{cc}3& 5\\ 1& 3\end{array}\right]$
Step 2
Characteristic equation of A
$|A-\lambda I|=0⇒|\begin{array}{cc}5-\lambda & 1\\ 1& 1-\lambda \end{array}|=0$
$\left(5-\lambda \right)\left(1-\lambda \right)-1=0$
$\lambda =1,5$
Characteristic equation of B
$|B-\lambda I|=0⇒|\begin{array}{cc}3-\lambda & 5\\ 1& 3-\lambda \end{array}|=0$
$\left(3-\lambda \right)\left(3-\lambda \right)-5=0$
$\left(3-\lambda {\right)}^{2}-5=0$
$9+{\lambda }^{2}-6\lambda -5=0$
${\lambda }^{2}-6\lambda +4=0⇒\lambda =0.164,5.236$
Step 3
Since Eigen values of the matrices are not equal, the given matrices are not similar.