**what is Identity matrix?**

An Identity matrix is a matrix in which the diagonals entries are 1 and off diagonals entries are zero. An Identity **matrix **is always a square matrix.

As we know that **square matrix** is in which a number of rows is equal to the number of columns. The identity matrix is denoted by I_{n\times n} where n by n shows the order of the identity matrix.it plays an important role in linear algebra since.

**If we multiply any real number with 1 then its remains unchanged.****If we multiply any matrix with identity matrix then its remains unchanged.**

**General form of identity matrix**

**Identity Matrix Examples**

Single matrix

I =\begin{bmatrix}1\end{bmatrix}

The order of the above matrix is 2 by 2

i_2 =\begin{bmatrix}1&0\\0&1\end{bmatrix}

The order of this matrix is 4 by 4

i_4 =\begin{bmatrix}1&0&0&0\\0&1&0&0\\0&0&1&0\\0&0&0&1\end{bmatrix}

The order of the above matrix is n by n

i_n =\begin{bmatrix}1&0&0&…&0\\0&1&0&…&0\\0&0&1&…&0\\…&…&…&…&…\\0&0&0&…&1\end{bmatrix}

**Notations of Identity Matrix**

**Notations of Identity Matrix**

The term **unit matrix** is widely used at an early age but now the term **identity matrix** has become a standard form. There is more notation used in different books such that in group theory the identity matrix is sometimes denoted by boldface one like **1. **Some mathematics books use U or E where U stands for unit matrix and E stand for a germen word Einheitsmatrix.

There is one more notation for identity matrix is KRONECKER DELTA.

If we have a matrix A with order m by n then it is a property of multiplication is that

l_mA= AI_n= A.

**properties of identity matrix**

- If we multiplying the two inverse matrices then we always get identity matrix in result such that
- If we multiply any matrix with identity matrix the result is identity matrix

I_mC = C = CI_n

- The identity matrix is the only matrix which is idempotent matrix with non-zero determinant that means it is the only matrix which have
- When the multiply by itself the result Is itself
- All of rows and columns are linearly independent
- The square root of an identity matrix is itself and this is the only positive definite square root
- It is always square matrix as the number of rows and the number of columns are equal