Question

Can we interchange columns in a matrix?

Answer 1

Hint: In mathematics, Matrix can be well-defined as the set of numbers which are arranged in the rows and the columns so as to form the rectangular array where the numbers arranged in the matrix are identified as the elements or the entries of the matrix.

Complete step-by-step answer:
The elements arranged horizontally are known as the rows while the elements arranged vertically are known as the columns.
Yes, we can interchange or swap the columns in the matrix.
When the interchange or the swapping of the columns or the rows results in the change of the sign in the determinant of the matrix. Therefore, to avoid the change in the sign of the determinant of the matrix, it is always recommended that to multiply the determinant with the number $( - 1)$

Note: Always remember and do not get confused between the determinants and the matrices. Determinant can be defined as the square matrix with the same number of rows and columns whereas the matrices can be well-defined as the rectangular grid of numbers and number of rows and the columns may or may not be the same.