# Identity matrix

The term **unit matrix** has also been widely used,^{[2]}^{[3]}^{[4]}^{[5]} but the term *identity matrix* is now standard.^{[6]} The term *unit matrix* is ambiguous, because it is also used for a matrix of ones and for any unit of the .^{[7]}

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.^{[9]}