Identity matrix

The indentity matrix is a square matrix that when multiplied by another matrix you don’t change the value of the other matrix. It’s common to abbreviate it it as just as , as just , etc, and they look like this:

Proof that I is a square matrix §

The dimensions of are , so let’s substitute those into the equation to get a visual picture of the dimensions.

We know the identity matrix must have columns:

We also know that the dimensions of the result matrix on the right comes from the rows of the first matrix and the columns of the second matrix.

Properties of §