1. The problem statement, all variables and given/known data 1) two linear transformations B and C are equivalent iff there exist invertible linear transformations P and Q such that PB=CQ 2) if A and B are equivalent then so are A' and B' in dual space 3) Do there exist linear transformations A and B such that A and B are equivalent but A^2 and B^2 are not? 4) Does there exist a linear transformation A such that A is equivalent to a scalar a but A is not equal to a? 3. The attempt at a solution I really don't know where to start. I know that if two l.ts. A and B are equivalent then (AB)^-1 = B^-1A^-1. But that's where I am now.