Graphical Construction of a 2x2 Matrix and Its Inverse
This Demonstration shows a pictorial representation of the relationship between a 2×2 matrix and its inverse. Drag the locators to determine two points; these define two vectors from the origin. The matrix has those vectors as its rows; it is shown on the lower left.
The inverse matrix is then shown on the lower right. The rows of the inverse matrix can be constructed from the two dashed vectors, which are orthogonal to the original vectors.
If no inverse to exists, this is indicated by "matrix is singular".