Finding a matrix and its transpose from a given matrix

Hi all, I'm new here. I'm currently doing a thesis on image compression and embedding. However, I'm stuck at a final part of my calculations.

Lets say you have a square matrix A. Taking the transpose of the matrix A you will get another square matrix A'.

Multiplying A by A' you get another square matrix B.

Example: A X A' = B

Now assuming you only have the matrix B given to you. How do you find the value of matrix A?

Hope you guys can help in this. Thanks alot.:)