Let A be an n×n matrix of real or complex numbers. Show that matrix A is invertible if which of the following satement are correct
a) The columns of A are linearly independent.
b) The columns of A span R^n . c) The rows of A are linearly independent.
d) The kernel of A is 0.
e) The only solution of the homogeneous equations Ax = 0 is x = 0.
f) The linear transformation TA : R^n → R n defined by A is 1-1. g) The linear transformation TA : R^n → R^n defined by A is onto. h) The rank of A is n.
THIS is the orginal question
I think a b c d e f g h i j all are correct...