The matrix which follows the conditions m=n is called?

The correct option is Square matrix.

To understand why this is the correct answer, let us break down the definition of a matrix and its dimensions step-by-step:

1. Dimensions of a Matrix:
A matrix is a rectangular array of numbers arranged in rows and columns. The size or dimension of a matrix is typically written as $m\times n$ (read as "m by n"), where:
• $m$ represents the number of horizontal rows.
• $n$ represents the number of vertical columns.

2. The Condition $m=n$:
When the condition is given as
$$m=n$$
it means that the number of rows is exactly equal to the number of columns.

3. Defining a Square Matrix:
By mathematical definition, any matrix that has the same number of rows and columns is called a square matrix. Because its height (rows) and width (columns) are equal, its shape resembles a square. Examples include $2\times 2$, $3\times 3$, or $k\times k$ matrices.

4. Why other options are incorrect:
• Rectangular matrix: A matrix where the number of rows is not equal to the number of columns ($m\ne n$).
• Diagonal matrix: A specific type of square matrix where all elements outside the main diagonal are zero. While it requires $m=n$, it has additional strict conditions on its elements.
• Scalar matrix: A specific type of diagonal matrix where all diagonal elements are equal. Like the diagonal matrix, it has extra conditions beyond just $m=n$.

Therefore, the most general term for any matrix satisfying $m=n$ is a Square matrix.