identity matrix

The identity matrix of size $n$ is the $n \times n$ square matrix with ones on the main diagonal and zeroes elsewhere.

I = (\begin{matrix} 1 & 0 & 0 & \dots & 0 \\ 0 & 1 & 0 & \dots & 0 \\ 0 & 0 & 1 & \dots & 0 \\ ⋮ & ⋮ & ⋮ & ⋱ & ⋮ \\ 0 & 0 & 0 & \dots & 1 \end{matrix})

The identity matrix is denoted $I_{n}$ when it is of size $n \times n$ , or simply $I$ when contextually obvious.

For any $m \times n$ matrix $A$ ,

I_{m} A = A = A I_{n}