An identity matrix is a square matrix with 1's going down the diagonal from the top left to the bottom right and 0's elsewhere. We use the letter I to denote an identity matrix.

If A is a square matrix, then B is the inverse of A if AB = BA = I, where I is an identity matrix.

(Note: In this case, we also say that A is the inverse of B.)

Finding the inverse of a matrix depends on its size.

• To find the inverse of a 2 x 2 matrix, use Formula H.

• To find the inverse of a 3 x 3 matrix (or any square matrix larger than 3 x 3), set up an augmented matrix: [A | I ]. Row reduce using Gauss-Jordan. If the result looks like [I | B], then B is the inverse of A.

• Graphing

• Algebraic Elimination

• Gauss-Jordan

• Matrix Equations

Note: If the problem tells you explicitly to use one of these methods specifically, you must use that method to get full credit. If the problem does not explicitly state which method to use, you may use any of these methods.