I had this question on a test, and I am wondering if I did it correctly.
"If A is a 3x3 matrix, AX = B has at least one solution for every B. Explain how to construct a 3x3 matrix C such that AC = I." (3 marks)
I basically said that since A and C are both square matrices, AC = I = CA, and thus C is just the inverse of A. So you could use the matrix inversion algorithm to find the inverse of A, and that would give you C.
Is that correct?