Invertible Matrix Theorem

Let . These statements are all equivalent

• is Invertible
• is invertible.
• is Row Equivalent to .
• has Pivots
• has only the trivial solution, i.e.
• The columns of A are Linearly Indepedent.
• A is Bijective
• The equation has a solution .
• has a left inverse
• A has a right inverse

• 0 is not an Eigenvalue of A