Answer
True
Work Step by Step
Assume the eigenvalues-eigenvector pairs $\{\lambda_i,v_i\}$ with $i=1,2,3...,n$.
Then the solutions to the vector differential equations $x′ = Ax$ and $x′ = Bx$ is $x(t)=c_1e^{\lambda_1t}v_1+c_2e^{\lambda_2t}v_2+...+c_ne^{\lambda_nt}v_n$.
Hence, the statement is true.
