Indicate whether the statement is always true or sometimes false. Justify your answer by giving a logical argument or a counter example

(i) If a linear system of n equations in n unknowns has two equations that are multiples of one another, then the system is inconsistent.

(ii) Every square matrix can be expressed as a product of elementary matrices.

(iii) Is it possible to have = without B being the inverse of A? Explain your reasoning

(iv) () is a diagonal matrix for every square matrix A.

(v) If () =0, then A is not expressible as a product of elementary matrices.