Square Matrix

A square matrix is a matrix in which the number of rows is equal to the number of columns. In other words, it is a matrix with an equal number of rows and columns. The matrix which follows the conditions m=n is called a square matrix.

Explanation:
- A matrix is a rectangular array of numbers or symbols arranged in rows and columns.
- The number of rows and columns in a matrix is denoted by m and n, respectively.
- In a square matrix, the number of rows is equal to the number of columns. Therefore, m=n.
- For example, a matrix with 3 rows and 3 columns is a square matrix because 3=3.
- Similarly, a matrix with 4 rows and 4 columns is also a square matrix because 4=4.

Properties of Square Matrix:
1. Number of rows is equal to the number of columns.
2. It is denoted by the order of the matrix, such as n x n.
3. All the diagonal elements of a square matrix are present from the top left to the bottom right and are called the principal diagonal.
4. The elements other than the diagonal elements are called off-diagonal elements.
5. The transpose of a square matrix remains a square matrix.
6. The determinant of a square matrix can be calculated.
7. The inverse of a square matrix exists if its determinant is not equal to zero.
8. The sum, difference, and product of two square matrices of the same order result in a square matrix of the same order.

Examples:
1. A = [2 4 6; 1 3 5; 7 9 8] is a square matrix because it has 3 rows and 3 columns (3=3).
2. B = [1 2 3; 4 5 6] is not a square matrix because it has 2 rows and 3 columns (2≠3).

Hence, the correct answer is option A) Square matrix.