# TI-BASIC:Identity

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Command Summary

Creates an n by n identity matrix.

Command Syntax

identity(n)

Menu Location

Press:

1. MATRX (on the 83) or 2ND MATRX (83+ or higher) to access the matrix menu.
2. LEFT to access the MATH submenu.
3. 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.