(a) For any two distinct column vectors

**u**and

**v**of M, the set {

**u**,

**v**} is lin. ind.

(b) The homogeneous system M

**x**=

**0**has only the trivial solution

(c) The system of equations M

**x**=

**b**has a unique solution for each real 5x1 column vectors

**b**

(d) The det(M) is nonzero

(e) There exists a 5x5 matrix N such that NM is the 5x5 identity matrix

b,c,d, and e are equivalent but why not a?

Since the matrix is nonsingular, the column vectors are lin ind.