1. Let $A, B \in M_{2}(\mathbb{C})$ such that: $A B=\left(\begin{array}{cc}10 & 30 \\ 4 & 20\end{array}\right)$ and $B A=\left(\begin{array}{cc}x & 60 \\ 2 & y\end{array}\right)$. Find $x$ and $y$.
1. $\left.\begin{array}{ll}\operatorname{det} A \cdot \operatorname{det} B=\operatorname{det}(A \cdot B) & 1 p \\ \operatorname{det}(B \cdot A)=\operatorname{det} B \cdot \operatorname{det} A & 1 p\end{array}\right\} \Rightarrow x y=200$

$$
\begin{aligned}
& \operatorname{tr}(A B)=\operatorname{tr}(B A) \Rightarrow x+y=30 \\
& \left\{\begin{array} { l } 
{ x + y = 3 0 } \\
{ x y = 2 0 0 }
\end{array} \Rightarrow \left\{\begin{array} { l } 
{ x = 2 0 } \\
{ y = 1 0 }
\end{array} \text { or } \left\{\begin{array}{l}
x=10 \\
y=20
\end{array}\right.\right.\right.
\end{aligned}
$$