### Addition , Substraction and Trace of two Matrix in Java.

Note: In linear algebra, the trace of an n-by-n square matrix A is defined to be the sum of the elements on the main diagonal (the diagonal from the upper left to the lower right) of A,

public static void main(String args[]) {
int a[][] = new int[3][3];
int b[][] = new int[3][3];
int sub[][] = new int[3][3];
int trace=0;
Scanner sc=new Scanner(System.in);

System.out.println("Enter First Matrix ");
for (int i = 0; i <= 2; i++)
{

for (int j = 0; j <= 2; j++)
{
a[i][j]=sc.nextInt();

}
}
System.out.println("Value of  First Matrix is ");
for (int i = 0; i <= 2; i++)
{

for (int j = 0; j <= 2; j++)
{
System.out.print(a[i][j]+" ");

}
System.out.println();
}

System.out.println("Enter Second Matrix ");
for (int i = 0; i <= 2; i++)
{

for (int j = 0; j <= 2; j++)
{
b[i][j]=sc.nextInt();

}
}
System.out.println("Value of Second Matrix is ");
for (int i = 0; i <= 2; i++)
{

for (int j = 0; j <= 2; j++)
{
System.out.print(b[i][j]+" ");

}
System.out.println();
}

for (int i = 0; i <= 2; i++)
{

for (int j = 0; j <= 2; j++)
{

}

}

for (int i = 0; i <= 2; i++)
{

for (int j = 0; j <= 2; j++)
{

}
System.out.println();
}

for (int i = 0; i <= 2; i++)
{

for (int j = 0; j <= 2; j++)
{
sub[i][j]=a[i][j]-b[i][j];

}

}

System.out.println("Substraction of Matrix is ");
for (int i = 0; i <= 2; i++)
{

for (int j = 0; j <= 2; j++)
{
System.out.print(sub[i][j]+" ");

}
System.out.println();
}

// Tracing Logic

for (int i = 0; i <= 2; i++)
{

for (int j = 0; j <= 2; j++)
{
if(i==j)
{
trace=trace+a[i][j];
}

}

}
System.out.println("Trace of Matrix A is  "+trace);

}

}

Output:

Enter First Matrix
1
2
3
1
2
3
1
2
3
Value of  First Matrix is
1 2 3
1 2 3
1 2 3
Enter Second Matrix
1
2
3
1
2
3
1
2
3
Value of Second Matrix is
1 2 3
1 2 3
1 2 3
2 4 6
2 4 6
2 4 6
Substraction of Matrix is
0 0 0
0 0 0
0 0 0

Trace of Matrix A is  6