If you want to visualize it better, let x=ac-bd and y=ad+bc; thus, -y=-(ad+bc)=-ad-bc.
Hi, I have managed to show that the sum of 2 matrices in one set is still in the same set, but I don't know how to show it when it is a multiplication . Thanks!
So, here is the problem:
Consider the set C of all matrices (with real entries) of the form
(sorry, I don't know how to code matrices! I'll separate each element with "|")
a | -b
b | a
Show that the product of two matrices in C is also in C.
So yeah, I have got up to here, but I don't know how to show that these is in the set C of matrices.
Let matrix M=
a | -b
b | a
So, M*M=
a^2-b^2 | -2ab
2ab | a^2-b^2
So this is what confuses me, it does not look like it was in the set?