From Galaxy Attack: Alien Shooter Wiki

Matrix displays 9 random Matrix Items. These pieces change every hour.

In order to win a prize from the Matrix, you must save up Matrix Tickets. You can obtain one ticket per day by playing a PvP match.

Every time you play on the Matrix, you win one of the 9 random items.

You can use jigsaw pieces to obtain a random piece from the displayed items. It can be a good idea to save up your jigsaw pieces until you see rewards on the Matrix that you are trying to obtain.