Identity Matrix

The identity matrix is a square matrix such that all the entries in the main diagonal are 1, and the rest of the entries are all 0. The identity matrix is denoted by $I$ in general. It is also denoted by $I_{n}$, where $n$ is the number of rows in the matrix. The $4 \times 4$ identity matrix $I_{4}$ is shown below:

$$I_{4} = \left[ \begin{array}{cccc} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{array} \right].$$

The unique property of the identity matrix is that multiplying it with another matrix (of a suitable order) does not change the matrix:

$$IA = A = AI.$$

Multiplying any matrix by its inverse yields the identity matrix:

$$A A^{-1} = I.$$

The identity matrix is a/an

• symmetric matrix
• diagonal matrix
• scalar matrix
• upper triangular matrix
• lower triangular matrix
• idempotent matrix
• involutory matrix
• orthogonal matrix .