The term unit matrix has also been widely used, but the term identity matrix is now standard. The term unit matrix is ambiguous, because it is also used for a matrix of ones and for any unit of the .
In terms of a notation that is sometimes used to concisely describe diagonal matrices, the identity matrix can be written as
The identity matrix is the only idempotent matrix with non-zero determinant. That is, it is the only matrix such that:
The principal square root of an identity matrix is itself, and this is its only positive-definite square root. However, every identity matrix with at least two rows and columns has an infinitude of symmetric square roots.