When the conjugate transpose of a complex square matrix is equal to the inverse of itself, then such matrix is called as **unitary**** matrix**. If Q is a complex square matrix and if it satisfies Q^{θ} = Q^{-1} then such matrix is termed as unitary. Please note that Q^{θ }and Q^{-1 }represent the conjugate transpose and inverse of the matrix Q, respectively.

The conjugate transpose of a matrix ‘Q’ can also be written as

.## Unitary matrix examples

The example of 2 x 2 unitary matrix is

The example of 3 x 3 unitary matrix is

**Note:** If A is a unitary matrix then it will satisfy AA^{θ} = I = A^{θ}A