# Proof of matrix conjugate (for the complex numbers)

## Homework Statement

Supposing that A*B is defined (where A and B are both matrices in the field of the complex numbers), show that the conjugate of matrix A * the conjugate of matrix B is equal to the conjugate of A*B.

None.

## The Attempt at a Solution

I'm stuck. I've already shown that for 2 complex numbers z1 and z2, the conjugate of z1 + the conjugate of z2 is equal to the conjugate of (z1+z2). I've also shown that the conjugate of z1 * the conjugate of z2 = the conjugate of (z1*z2). My prof says to use the above to help with the proof.

I'm quite inexperienced with proofs, so any hint or tip would be extremely appreciated. Thanks.

lanedance
Homework Helper
you could try writing out th sum as elements

Ie say you have

C = AB

then for and elemnt of C at row i, & column j, each cij is given by the sum
cij = (sum over k) aikbkj

This reduces the matrix multiplication to addition & multiplication of individual complex numbers

HallsofIvy