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## Homework Statement

This is a GRE practice problem I was reading through that confused me.

36. Let M be a 5x5 real matrix. Exactly four of the following five conditions on M are equivalent to each other.

Which of the five conditions is equivalent to NONE of the other four?

(A) For any two distinct column vectors u and v of M, the set

{u,v} is linearly independent.

(B) The homogeneous system Mx= 0 has only the trivial solution.

(C) The system of equations Mx=b has a unique solution for each real 5x1 column vector b.

(D) The determinant of M is nonzero.

(E) There exists a 5x5 real matrix N such that NM is the 5x5 identity matrix.

## Homework Equations

IMT

## The Attempt at a Solution

I was under the impression that all of these were equivalent via IMT. Am I misreading something? Thanks for the help!