How to Find the Inverse of a 3X3 Matrix

The inverse of a matrix is defined as follows: If A and B are two n x n matrices, A and B are inverses of each other if AB = BA = I; I being the n x n identity matrix. Finding the inverse of a matrix only requires a basic knowledge of linear algebra and a simple algorithm.

Difficulty: Moderate

Instructions

The Steps

1. Set up the original matrix in augmented form with the identity matrix next to it.

2. Row reduce the original matrix to form the identity matrix on its side.

3. The row reductions will produce the inverse matrix on the opposite side of the augmented matrix.

4. Check that you've found the correct matrix by row reducing the inverse back to the identity matrix. If you get the original matrix, you've found the correct answer.

5. Another way to check is to multiply the two matrices together. AB should equal the identity matrix if you found the correct inverse since AB = BA = I.

References

• Inverse of a Matrix

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