# TI-BASIC:Identity

**Command Summary**

Creates an *n* by *n* identity matrix.

**Command Syntax**

identity(*n*)

**Menu Location**

Press:

- MATRX (on the 83) or 2ND MATRX (83+ or higher) to access the matrix menu.
- LEFT to access the MATH submenu.
- 5 to select identity(, or use arrows.

TI-83/84/+/SE

1 byte

The identity( command generates an identity matrix: that is, a matrix [B] such that for any other matrix [A], [A]*[B]=[A] (if [A] is the right size to make the multiplication valid).

The identity matrix is square (that is, the row dimension equals the column dimension); all of its elements are 0 except for the elements along the main diagonal (the diagonal going from top left to bottom right).

The command itself takes one argument: the size of the matrix, used for both row and column size, that is, identity(*n* creates an *n* by *n* matrix.

:dim([A] :identity(Ans(2→[B] :[A][B]=[A] // should always return 1, meaning 'true'

# Optimization

The identity( command can be used as a quick way to create an empty square matrix: 0identity(*n* will create an *n* by *n* matrix containing only 0 as an element. This is faster and smaller than the Dim( and Fill( commands used for the same purpose:

:{5,5→dim([A] :Fill(0,[A] can be :0identity(5→[A]

# Error Conditions

**ERR:INVALID DIM**occurs if the size is not an integer 1-99. In practice, however, even identity(37 requires more free RAM than the calculator ever has.