The discussion revolves around the relationship between the characteristic polynomials of two nXn matrices A and B, specifically under the condition that A is invertible. The original poster attempts to prove that P_{AB}(x) equals P_{BA}(x) based on properties of determinants.
The discussion is ongoing, with participants providing hints and questioning assumptions. Some express frustration with direct answers being given instead of guidance, indicating a focus on exploring the problem rather than resolving it outright.
There is a mention of forum guidelines that discourage providing complete solutions, emphasizing the need for hints and guidance instead. The original poster's assumption about the determinant of an invertible matrix being zero is also under scrutiny.
Dick said:netheril96, you are supposed to give hints and help. Not work out people's problems for them. Read the forum guidelines.
talolard said:Homework Statement
Let A and B be to nXn matrices and A is invertible. Prove: [tex]P_{AB}(x)=P_{BA}(x)[/tex]The Attempt at a Solution
Since A is invertible we have det(A)=0. [tex]det(AB)= det(A)det(B)=0det(B)=0 ->P_{AB}(x)=P_{BA}(x)=0[/tex]
Is that correct?
[
netheril96 said:But this problem is so easy that the only hint I can give is the direct answer
Dick said:It's not 'so easy' for a lot of people. If the only hint you can think of is to give the solution, don't. Find another thread to work on. Could you remove the post with your proof in it please?
netheril96 said:Deleted