Question 178
The matrices $A, B \in \mathcal{M}_2(\mathbb{R})$ have the property $(A - B)^2 = O_2$.
a) Show that $\det(A^2 - B^2) = (\det(A) - \det(B))^2$.
b) Show that $\det(AB - BA) = 0$ if and only if $\det(A) = \det(B)$.
a) Show that $\det(A^2 - B^2) = (\det(A) - \det(B))^2$.
b) Show that $\det(AB - BA) = 0$ if and only if $\det(A) = \det(B)$.