[tex]A^2 = A \cdot A = \left(\begin{array}{cc}4&-5\\3&-4\end{array}\right) \cdot \left(\begin{array}{cc}4&-5\\3&-4\end{array}\right) = \left(\begin{array}{cc}1&0\\0&1\end{array}\right) = I_2\\\\
A^3 = A^2\cdot A = I_2\cdot A = A\\
A^4 = A^2\cdot A^2=I_2\cdot I_2 = I_2\\
\text{Deci, pentru n par }A^n = I_2 \text{, iar pentru n impar } A^n = A\\
\text{Pentru n = 2020, }A^{2020} = I_2\\
det(A^{2020}) = det(I_2) = 1[/tex]
