# Conjugate of a Matrix – Example & Properties

Conjugate of a matrix is the matrix obtained from matrix ‘P’ on replacing its elements with the corresponding conjugate complex numbers. It is denoted by

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## Conjugate of a matrix example

Let Q is a matrix such that

Now, to find the conjugate of this matrix Q, we find the conjugate of each element of matrix Q i.e.

This is the conjugate of a 2 x 2 matrix Q.

## Conjugate of a matrix properties

The conjugate of matrices P and Q are

. Then,

If P is a purely imaginary matrix

If P is a real matrix

where ‘a’ is any complex number.

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