Let A10×10 matrix. Given that A^{2020}=0. Let m(x) be the minimal polynomial of A. By Cayley-Hamilton, the degree of mm is atmost 10. By the propert of minimal polynomial m(x) devides x2020. Then the possibilty of are m(x)=x^{k} for some k=1,2,⋯ ,10.

Case 1: If $k=10, $ and since A satisfies its minial polynomial we have A10=0.

Case 2: If k\(A^{10}=A^{10}-kA^{k}=A10-k\times0=0.\)

In Any case we have A^{10}=0.

Case 1: If $k=10, $ and since A satisfies its minial polynomial we have A10=0.

Case 2: If k\(A^{10}=A^{10}-kA^{k}=A10-k\times0=0.\)

In Any case we have A^{10}=0.