I am confused with the row/column operations on matrices aand determinants. if we are doing row operation on a determinant can we switch to column operation as the next step (if reqd.) in the same question? Can we do the same kind of procedure in a matrix?

Determinant:

 

The interchange of row and columns does not affect the value of the determinant.

Hence we can use either row or column transformation or both of them in the same problem

 

Matrix:

A matrix does not have a value. It is an arrangement of numbers in rows and columns, hence the position of an element is very important.

So we cannot use row and column operations randomly.

 

If you are refering to 'finding inverse by elementary transformations',

then you can use only row transformations for the pre-factor and only column transformations for post factor in the matrix equation.