# Identity Matrix

### What is an Identity Matrix?

What is an Identity Matrix?

The identify matrix is a square matrix is where all the principle diagonal is 1s and the rest are 0s. The principle diagonal is from top left to bottom right. The secondary diagonal is from bottom left to top right.

The identity matrix is like the multiplication identity. We denote the identity matrix as In , where n is the order of the square matrix.

### Examples Examples:

The identity matrix keeps going and going so 5, 6, 7, and ....

### Properties

1. An identity is always a square. That means the rows and columns must be equal.

2. Multiplying a matrix by the identity results in the original matrix, so A * I = A or I * A = A. This is very similar to the multiplicative identity like 5 and (1/5).

3. Multiplying a matrix by its inverse results in the identity matrix. So A * A-1 = 1 or A-1 * A = 1.

4. The trace is equal to the sum of the principal diagonal so the trace is equal to n or the order.

5. The determinant of any identity matrix is equal to 1.

## Live Worksheet

Here is the link if you prefer.