Inverse of a 2x2 matrix for JEE

Formula

\[\begin{bmatrix}a&b\\c&d\end{bmatrix}^{-1}=\frac{1}{ad-bc}\begin{bmatrix}d&-b\\-c&a\end{bmatrix}\]

Variables: \(a,b,c,d\): entries of the matrix.

Conditions: \(ad-bc\ne 0\).

Direct inverse calculation, solving two-variable linear systems.