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?