Question 30
The $2\times2$ square matrices $A,B$ satisfy
$$AB=A^2B^2-(AB)^2,\qquad\det B=2.$$
a) Prove that $A$ is not invertible.
b) Calculate $\det(A+2B)-\det(B+2A)$.
$$AB=A^2B^2-(AB)^2,\qquad\det B=2.$$
a) Prove that $A$ is not invertible.
b) Calculate $\det(A+2B)-\det(B+2A)$.