1.7.6 Linear transformations

Problem: Given the operators \( A x=\left\{x_{2}-x_{3}, x_{1}, x_{1}+x_{3}\right\} \), \( B x=\left\{x_{2}, 2 x_{3}, x_{1}\right\} \). Find the operator \( \left(B^{2}-2 A\right) \).