Write a Java program to create (4 x 4) 2D double array in the name of ‘A’ using new.Read the values at runtime. Perform the following operations over matrix ‘B’ and ‘C’;B (2 x 3) =C (4 x 2) =(a) If ‘A’ is diagonal matrix then perform (B + C)(b) If ‘A’ is non-diagonal matrix then perform (B * C)(c) If ‘A’ is identity matric then display the transpose matrix ‘C’

Sure, here is a Java program that performs the operations you described:

import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        double[][] A = new double[4][4];
        double[][] B = new double[2][3];
        double[][] C = new double[4][2];

        System.out.println("Enter the elements of A:");
        for (int i = 0; i < 4; i++) {
            for (int j = 0; j < 4; j++) {
                A[i][j] = scanner.nextDouble();
            }
        }

        System.out.println("Enter the elements of B:");
        for (int i = 0; i < 2; i++) {
            for (int j = 0; j < 3; j++) {
                B[i][j] = scanner.nextDouble();
            }
        }

        System.out.println("Enter the elements of C:");
        for (int i = 0; i < 4; i++) {
            for (int j = 0; j < 2; j++) {
                C[i][j] = scanner.nextDouble();
            }
        }

        if (isDiagonal(A)) {
            // Perform B + C
            // Note: This operation is not possible as B and C have different dimensions
        } else if (isIdentity(A)) {
            // Display the transpose of C
            double[][] transposeC = transpose(C);
            printMatrix(transposeC);
        } else {
            // Perform B * C
            // Note: This operation is not possible as B and C have incompatible dimensions for multiplication
        }
    }

    public static boolean isDiagonal(double[][] matrix) {
        for (int i = 0; i < matrix.length; i++) {
            for (int j = 0; j < matrix[i].length; j++) {
                if (i != j && matrix[i][j] != 0) {
                    return false;
                }
            }
        }
        return true;
    }

    public static boolean isIdentity(double[][] matrix) {
        for (int i = 0; i < matrix.length; i++) {
            for (int j = 0; j < matrix[i].length; j++) {
                if (i == j && matrix[i][j] != 1) {
                    return false;
                }
                if (i != j && matrix[i][j] != 0) {
                    return false;
                }
            }
        }
        return true;
    }

    public static double[][] transpose(double[][] matrix) {
        double[][] transpose = new double[matrix[0].length][matrix.length];
        for (int i = 0; i < matrix.length; i++) {
            for (int j = 0; j < matrix[i].length; j++) {
                transpose[j][i] = matrix[i][j];
            }
        }
        return transpose;
    }

    public static void printMatrix(double[][] matrix) {
        for (double[] row : matrix) {
            for (double element : row) {
                System.out.print(element + " ");
            }
            System.out.println();
        }
    }
}

Please note that the operations B + C and B * C are not possible with the given dimensions of B and C. The addition of two matrices is only possible if they have the same dimensions, and the multiplication of two matrices is only possible if the number of columns in the first matrix is equal to the number of rows in the second matrix.