How to generate unique chars when populating a 2D array?

How do I make it so that when I output the grid when I run the code, no two numbers or letters will be the same? When I currently run this code I could get 3x "L" or 2x "6", how do I make it so that they only appear once?

package polycipher;

import java.util.ArrayList;

public class Matrix {
private char[][] matrix = new char[6][6];
private int[] usedNumbers = new int[50];

{for(int x = 0; x < usedNumbers.length; x++) usedNumbers[x] = -1;}

private final char[] CIPHER_KEY = {'A','D','F','G','V','X'};
private final String validChars = "ABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789";

public Matrix() {
    int random;
    for(int i = 0; i < CIPHER_KEY.length; i++) {
        for(int j = 0; j < CIPHER_KEY.length; j++) {
            validation: while(true) {
                random = (int)(Math.random()*validChars.length()-1);
                for(int k = 0; k < usedNumbers.length; k++) {
                    if(random == usedNumbers[k]) continue validation;
                    else if(usedNumbers[k]==-1) usedNumbers[k] = random;
                }
                break;
            }
            matrix[i][j] = validChars.split("")[random].charAt(0);  
        }
    }
}

public String toString() {
    String output = "   A D F G V X\n";
    for(int i = 0; i < CIPHER_KEY.length; i++) {
        output += CIPHER_KEY[i] + "  ";
        for(int j = 0; j < CIPHER_KEY.length; j++) {
            output += matrix[i][j] + " ";
        }
        output += "\n";
    }
    return output;
}
}