设计一个Java程序，完成以下3个功能： （1）任意输入m和n，生成一个m*n的矩阵A，里面的数值由输入完成，输出A； （2）生成A的转置矩阵B，输出B； （3）由A与B相乘，得出矩阵C，输出C。

为了设计一个Java程序来完成上述三个任务，我们可以创建一个`Matrix`类，包含相关的操作方法。以下是程序的大致结构：

import java.util.Scanner;

class Matrix {
    private int[][] elements;
    private int rows;
    private int cols;

    // 构造函数，接受行数和列数以及用户输入的元素
    public Matrix(int m, int n) {
        this.rows = m;
        this.cols = n;
        elements = new int[rows][cols];
        Scanner scanner = new Scanner(System.in);
        System.out.println("请输入矩阵A的元素:");
        for (int i = 0; i < rows; i++) {
            for (int j = 0; j < cols; j++) {
                elements[i][j] = scanner.nextInt();
            }
        }
        scanner.close();
    }

    // 方法用于获取矩阵A
    public void display() {
        for (int[] row : elements) {
            for (int elem : row) {
                System.out.print(elem + " ");
            }
            System.out.println();
        }
    }

    // 转置矩阵的方法
    public Matrix transpose() {
        Matrix transposed = new Matrix(cols, rows);
        for (int i = 0; i < rows; i++) {
            for (int j = 0; j < cols; j++) {
                transposed.elements[j][i] = elements[i][j];
            }
        }
        return transposed;
    }

    // 相乘并返回结果矩阵C
    public Matrix multiply(Matrix other) throws IllegalArgumentException {
        if (cols != other.rows) {
            throw new IllegalArgumentException("矩阵A的列数应等于矩阵B的行数");
        }
        Matrix result = new Matrix(rows, other.cols);
        for (int i = 0; i < rows; i++) {
            for (int j = 0; j < other.cols; j++) {
                int sum = 0;
                for (int k = 0; k < cols; k++) {
                    sum += elements[i][k] * other.elements[k][j];
                }
                result.elements[i][j] = sum;
            }
        }
        return result;
    }

    // 主方法来运行整个程序
    public static void main(String[] args) {
        Scanner input = new Scanner(System.in);
        System.out.println("请输入矩阵A的行数和列数(例如: 3 4):");
        int m = input.nextInt();
        int n = input.nextInt();
        Matrix matrixA = new Matrix(m, n);

        Matrix transposeB = matrixA.transpose();
        transposeB.display();

        try {
            Matrix matrixB = new Matrix(n, m); // B的构造函数需要m和n互换
            Matrix matrixC = matrixA.multiply(matrixB);
            matrixC.display();
        } catch (IllegalArgumentException e) {
            System.out.println(e.getMessage());
        }
    }
}