Mathematics
Matrix Inverses and Solving Systems of Linear Equations
Quick fact
Inverting a 2x2 matrix is quick: swap the diagonal, negate the off-diagonal, and divide by the determinant. If the determinant is zero, no inverse exists—and the system either has no solution or infinitely many.
Why this is interesting
You know elimination, but what if you could just 'divide' by a matrix? That's exactly what an inverse lets you do—turning a system of equations into a one-step solution.