Matrix Repeating Background

Make a new document. Make the dimensions to be whatever you want. I chose 150x150 pixels. Follow the matrix tutorial to get matrix effect first.

When you're finished with the matrix tutorial, go to Image > Canvas Size. Set the canvas to double the current size. In my case, it's 300x300. Make sure you select the top left corner of the anchor grid.

After you're done, duplicate the current matrix layer. Then go to Filter > Other > Offset. Make the horizontal and vertical offsets half of your canvas size.

When you're ready, merge the two layers together. Then duplicate it. Then go to Edit > Transform > Flip Vertical. Then merge the duplicated layer with the original. Finally, go to Edit > Define Pattern. Name it 'Matrix Background.' Congratulations, you're done! To fill a layer with the pattern you just created, go to Edit > Fill. Then find 'Pattern' in the drop-down menu, and find the pattern thumbnail.