Although it is claimed that a = b, c, d, e, ., j, the justifications only show that a = b, c, d, e, .

Although it is claimed that a <=> b, c, d, e, . . ., j, the justifications only show that a => b, c, d, e, . . ., j. That is, each of the 9 steps assume that A is invertible and then show one of the other statements logically follows. However, to show completely demonstrate logical equivalence it is necessary to show that b, c, d, . . ., j => a. That is assume the one of the statements and show that the statement logically implies (a).Please explicitly discuss how the justification demonstrate that the statement are logically equivalent.