I have a question for which I need help:
Let M consist of all 2*2 matrices of the form
Show that the product of the two matrices in M is a matrix in M.
Here's my attempt:
.: the product of two matrices in M is a matrix is M. Simple enough!
[a b][a b] = [a^2-b^2 ab+ab]
[-b a][-b a] [-ab-ab -b^2+a^2]
= [a^2-b^2 2ab]
However, the question goes on to say:
Let * denote the binary operation of matrix multiplication on M. Show that I is the identity element of M under *, and find the inverse of any arbitrary matrix of M.
Find two distinct elements x E M which satisfy x * x * x * x = I.
I don't know how to do this. Please help!