Inverse Axiom

My group is GL2(R), which by definition is the set of all 2x2 invertible matrices with real entries under matrix multiplication. Therefore, by its definition every element in GL2(R) has an inverse.

Formally, given a matrix A = $\begin{pmatrix}a & b \\c & d \end{pmatrix}$, A-1 = $\frac{1}{ad-bc}\begin{pmatrix}d & -b \\-c & a \end{pmatrix}$
Therefore, as long as ad-bc does not equal zero, A will have an inverse.
Therefore, as long as the determinant of A does not equal zero, A will have an inverse.
This emplies my group is the set of all 2x2 matrices with determinant not equal to zero.

page revision: 2, last edited: 14 Oct 2009 21:05