How do you perform range compression of SAR data on a 2D matrix?

I am building a Matlab program to process RADARSAT-1 data that came with this book.

The book describes the steps to creating SAR image as follows

I am currently implement the range compression step. For my matched filter computation I am performing a range FFT by transposing each row of the 2D matrix that represents my image first then taking the FFT of that.I understand what I need to do to perform my matched filter computation. My question is more related to how to do it in matlab on a 2D matrix. My 2D matrix is 1536×2048 where 2048 is the number of columns which represents my fast time samples or range cells.Currently I am transposing each row so I can perform the fft on the rows of the 2D matrix in order to do the matched filter computation. Is that the right thing to do? If not what should I do?

Lastly, how can I confirm that my range compression code works?