Last updated: Jan. 2nd, 2019
Show the inverse matrix of a 2x2 matrix

is

, where $|A| = 0$.

Proof

To find the inverse marix of a 2x2 matrix $A$,
we use the property that
the inverse matrix is the product of the reciprocal of the determinant and the adjugate matrix, i.e.,

, where $\tilde{A}$ is the adjugate matrix of $A$.
The determinant of $A$ is