The number of rows and columns in a matrix expressed as row columns. The matrix below comprises 2 rows and 3 columns, for a total of 23 dimensions. “Two by three,” is read aloud. The number of columns in the first matrix must equal the number of rows in the second matrix for matrix multiplication to be defined.

We use the dot product of a row in A and a column in B to find A B AB AB. Simply write the components of a row as columns and the elements of a column as rows to calculate the transpose of a matrix.

The 2×2 Matrix is a decision-making technique in which possibilities are plotted on a two-by-two matrix. A four-blocker is also known as a magic quadrant. A simple square divided into four equal quadrants forms the matrix diagram. Each axis indicates a criterion for making a decision, such as a price or effort.

Determinants are special numbers computed from the square matrix in matrices. For a matrix with three rows and three columns, the determinant of a 3 x 3 matrix is determined. The determinant is represented by vertical lines on either side of the sign, such as | |.

```
import java.util.*;
class Main
{
public static void main(String args[])
{
Scanner sc = new Scanner(System.in);
int i,j,row,col,temp;
System.out.println("Enter the number of rows");
row = sc.nextInt();
System.out.println("Enter the number of columns");
col = sc.nextInt();
int[][] mat = new int[row][col];
System.out.println("Enter the elements of the matrix") ;
for(i=0;i<row;i++)
{
for(j=0;j<col;j++)
{
mat[i][j] = sc.nextInt();
}
}
System.out.println("The elements of the matrix") ;
for(i=0;i<row;i++)
{
for(j=0;j<col;j++)
{
System.out.print(mat[i][j]+"\t");
}
System.out.println("");
}
for(i=0;i<row;i++)
{
for(j=0;j<i;j++)
{
temp = mat[i][j];
mat[i][j] = mat[j][i];
mat[j][i] = temp;
}
}
System.out.println("The transpose of the matrix is ") ;
for(i=0;i<row;i++)
{
for(j=0;j<col;j++)
{
System.out.print(mat[i][j]+"\t");
}
System.out.println("");
}
}
}
```

Output:

Enter the number of rows

2

Enter the number of columns

2

Enter the elements of the matrix

45

67

78

34

The elements of the matrix

45 67

78 34

The transpose of the matrix is

45 78

67 34