Java Program to determine whether a given matrix is an identity matrix

In this program, we need to check whether the given matrix is an identity matrix.

Identity Matrix

Java Program to determine whether a given matrix is an identity matrix

A matrix is said to be an identity matrix if it is a square matrix in which elements of principle diagonal are ones, and the rest of the elements are zeroes.

Algorithm

  • STEP 1: START
  • STEP 2: DEFINE rows, cols
  • STEP 3: SET flag =true
  • STEP 4: INITIALIZE matrix a[][] ={{1,0,0},{0,1,0}, {0,0,1}}
  • STEP 5: rows = a.length
  • STEP 6: cols = a[0].length
  • STEP 7: if(rows!=cols)
                then
              PRINT “Matrix should be a square matrix”
             else
           go to step 8
  • STEP 8: REPEAT STEP 9 to STEP 11 UNTIL i<rows
                //for(i=0; i<rows; i++)
  • STEP 9: REPEAT STEP 10 to STEP 11 UNTIL j<cols
                //for(j=0; j<cols; j++)
  • STEP 10: if(i==j && a[i][j]== 1) then
                SET flag =false
                break
  • STEP 11: if( i!=j && a[i][j]!=0)
                SET flag = false
                break
  • STEP 12: if(flag)
                then PRINT (“Given matrix is an identity matrix”)
                else
                PRINT (“Given matrix is not an identity matrix”)
  • STEP 13: END

Program:

  1. public class IdentityMatrix     
  2. {    
  3.     public static void main(String[] args) {    
  4.         int rows, cols;    
  5.         boolean flag = true;    
  6.             
  7.         //Initialize matrix a    
  8.         int a[][] = {       
  9.                         {1, 0, 0},    
  10.                         {0, 1, 0},    
  11.                         {0, 0, 1}    
  12.                     };    
  13.             
  14.         //Calculates the number of rows and columns present in the given matrix    
  15.     
  16.           rows = a.length;    
  17.         cols = a[0].length;    
  18.             
  19.         //Checks whether given matrix is a square matrix or not    
  20.         if(rows != cols){    
  21.             System.out.println(“Matrix should be a square matrix”);    
  22.         }    
  23.         else {    
  24.             //Checks if diagonal elements are equal to 1 and rest of elements are 0    
  25.             for(int i = 0; i < rows; i++){    
  26.                 for(int j = 0; j < cols; j++){    
  27.                   if(i == j && a[i][j] != 1){    
  28.                       flag = false;    
  29.                       break;    
  30.                   }    
  31.                   if(i != j && a[i][j] != 0){    
  32.                       flag = false;    
  33.                       break;    
  34.                   }    
  35.                 }    
  36.             }    
  37.                 
  38.             if(flag)    
  39.                 System.out.println(“Given matrix is an identity matrix”);    
  40.             else    
  41.                 System.out.println(“Given matrix is not an identity matrix”);    
  42.         }    
  43.     }    
  44. }    

Output:

Given matrix is an identity matrix

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