Can the rows and columns of the matrix be interchanged at will?

Can the rows and columns of the matrix be interchanged at will? Introduction is as follows:

Two rows or two columns of a matrix can be interchanged without changing the sign like a determinant.

Generally speaking, a matrix can be regarded as the coefficient of a set of equations to some extent. In essence, a row of equations constitutes a matrix. Therefore, it can be considered that swapping the position of an equation in a set of equations does not affect the final solution of the equation, and it is the same when it is applied to a matrix, so swapping rows and columns does not affect the matrix.

Specific introduction:

In mathematics, a matrix is a group of complex numbers or real numbers arranged in a rectangular array, which originated from a square matrix composed of coefficients and constants of an equation. Two rows or two columns of the commutative matrix are one of the elementary transformations of the matrix; If matrix A is transformed into matrix B by finite elementary row transformation, then matrix A is equivalent to matrix B; If matrix A is transformed into matrix B by finite elementary column transformation, then matrix A is equivalent to matrix B; If matrix A is transformed into matrix B by finite elementary transformation, then matrix A is equivalent to matrix B. ..

Matrix introduction:

In mathematics, a matrix is a group of complex numbers or real numbers arranged in a rectangular array, which originated from a square matrix composed of coefficients and constants of equations. This concept was first put forward by British mathematician Kelly in19th century. Matrix is a common tool in applied mathematics such as advanced algebra and statistical analysis.

In physics, matrices have applications in circuit science, mechanics, optics and quantum physics. In computer science, three-dimensional animation also needs matrix. Matrix operation is an important problem in the field of numerical analysis.