Finding Matrices that you can multiply wrong, right
Summary
The post investigates a playful linear-algebra puzzle: whether one can choose nxn matrices A and B so that AB equals a simple function of A and B, and what structural conditions arise from such constructions. It explores eigenvectors, eigenvalues, and relationships like Λ_A Λ_B = 10 Λ_A + Λ_B, and discusses expressing B as a polynomial in A and using determinant constraints, while pointing to experiments and related literature.