Question: Show that the equation Ax = x can be rewritten as (A - I)x = 0
where A is a n by n matrix and x is a n by 1 matrix.
My (probably incorrect) answer:
Ax = x
Ax(x^-1) = x(x^-1)
A(xx^-1) = xx^-1
AI = I
A = I
A - I = 0
(A - I)x = 0x
(A - I)x = 0
Might anyone tell me how I should be going about solving this?