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Код
import java.util.Random;

public class Matrix {

    private static Random random = new Random();

    public static void main(String[] args) {
        int[][] matrix1 = createMatrix(5, 5);
        int[][] matrix2 = createMatrix(5, 5);

        System.out.println("Matrix 1, original:");
        showMatrix(matrix1);
        System.out.println("Matrix 2, original:");
        showMatrix(matrix2);

        int column1 = getColumnWithMinValue(matrix1);
        int column2 = getColumnWithMaxValue(matrix2);

        swapColumns(matrix1, column1, matrix2, column2);

        System.out.println("Matrix 1, swapped:");
        showMatrix(matrix1);
        System.out.println("Matrix 2, swapped:");
        showMatrix(matrix2);

    }

    private static int[][] createMatrix(int rowCount, int columnsCount) {
        int[][] matrix = new int[rowCount][columnsCount];
        for (int i = 0; i < matrix.length; i++) {
            for (int j = 0; j < matrix[i].length; j++) {
                matrix[i][j] = random.nextInt(100);
            }
        }
        return matrix;
    }

    private static void showMatrix(int[][] matrix) {
        for (int i = 0; i < matrix.length; i++) {
            for (int j = 0; j < matrix[i].length; j++) {
                System.out.printf("%3d ", matrix[i][j]);
            }
            System.out.print("\n");
        }
    }

    private static int getColumnWithMinValue(int[][] matrix) {
        int row = 0;
        int column = 0;
        for (int i = 0; i < matrix.length; i++) {
            for (int j = 0; j < matrix[i].length; j++) {
                if (matrix[i][j] < matrix[row][column]) {
                    row = i;
                    column = j;
                }
            }
        }
        return column;
    }

    private static int getColumnWithMaxValue(int[][] matrix) {
        int row = 0;
        int column = 0;
        for (int i = 0; i < matrix.length; i++) {
            for (int j = 0; j < matrix[i].length; j++) {
                if (matrix[i][j] > matrix[row][column]) {
                    row = i;
                    column = j;
                }
            }
        }
        return column;
    }

    private static void swapColumns(int[][] matrix1, int column1, int[][] matrix2, int column2) {
        for (int i = 0; i < matrix1.length; i++) {
            int value = matrix1[i][column1];
            matrix1[i][column1] = matrix2[i][column2];
            matrix2[i][column2] = value;
        }
    }

}