In order to find the inverse of matrices larger that 2x2, we need a better method. If A is invertible and of size n×n, then we can find the matrix by the following method:

  1. Set up a matrix [A|I], a n×2n matrix where the left half is A and the right half is the identity matrix size n.
  2. Perform elementary row operations to reduce the left side to the identity matrix, while also performing those same operations on the right side.
  3. If A is invertible, when the left side is reduced to the identity matrix, the right side will be A-1. If the left side cannot be reduced to I, then A is not invertible.

Let's see an example of this below:


References & Resources