The identity matrix and its properties

The identity matrix is a square matrix that has 1’s along the main diagonal and 0’s for all other entries. This matrix is often written simply as I, and is special in that it acts like 1 in matrix multiplication. In this lesson, we will look at this property and some other important idea associated with identity matrices.

1 Multiplying any matrix by the identity results in the matrix itself

2 The product of two inverse matrices is always the identity

One concept studied heavily in mathematics is the concept of invertible matrices, which are those matrices that have an inverse. By definition, when you multiply two matrices that are inverses of each other, then you will get the identity matrix.

Summary
The identity matrix is a fundamental idea when working with matrices – whether you are working with just multiplication, inverses, or even solving matrix equations. As you study these types of topics, be sure that you have a fundamental understanding of this matrix.