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Hi
I am new to this website.  I am not a student. I am retired from International Paper and am reviewing my math because I would like to lean quantum mechanics. ( Always been interested in this subject. ) My only saving grace is my math degree so I thought I would start there and first review my math books from ages ago.  I am stuck on a math problem I will now post and also have a general question on a possible recommendation as to quantum mechanics introductory textbooks.

Here is the problem:  ( From by linear algebra textbook review. )
For a general nxn matrix  called A with specific eigenvalues denoted by L1,...,Ln. The identity matrix will be denoted I and L will represent lambda symbol  from within the characteristic polynomial.
How can it be proved that  determinant(A - LI) = (-1)^n(L-L1)(L-L2)...(L-Ln)
That's it.
I can see that the factor theorem will be useful here to pull out the factors (L-Li) i=1,2,...,n-1
I can also see that determinant(LI-A) = (-1)determinant(A-LI).  That is one is the negative of the other but I am having showing how the determinant of (A-LI) will factor with a (-1)^n. When I start taking out each and work out all the possibilities for the last factor I cannot show it will always be "nice". ( i.e (L-Ln) * (-1)^n.
                                                                          Thank you so much !
                                                                           Julius
                                                                     jmazza@peoplepc.com
My other question is a recommendation for a good introductory quantum mechanics book that integrates and explains the mathematics along with the physics. I have found on BarnesandNobel a book titled .  Quantum Mechanics: A Conceptual Introduction" but there are customer reviews. In fact there is another one called Quantum Mechanics: An Accessible Introduction by Robert Scherrer and also this one has no custormer reviews. Nor are there any customer reviews on amazon.com. Maybe someone has gone through this venture to learn quantum mechanics and can recommend a textbook with worked examples and self contained mathematics.  Keep in mind I do know calculus since I have a math degree.
                                                                             Thank you again!