Question

Fie A apartine M2020 o matrice inversabila astfel determinantul matricei adjunte este (poza).Sa se calculeze determinantul matricei A

Answer 1

Răspuns:

$AA^{*}=(\det A)\cdot I_n$. Deci $\det(AA^*)=\det A\det A^* = (\det A)^n$, de aici rezulta ca $\det A^*=(\det A)^{n-1}$.

n=2020, deci $\det A^* =(\det A)^{2019}$.

Inlocuind, avem $(\det A)^{2019}=2019^{673}$, deci $\det A=2019^{\frac{673}{2019}}=2019^{\frac{1}{3}}=\sqrt[3]{2019}$.