Determinant - Elementary operations in Matrix Equation

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Why that highlighted condition is true ? How can we prove it ?
I have no idea about elementary operation in this specific way i.e matrix equation and also in row operation we have to do something different enter image description here

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Elementary column operations on a matrix are equivalent to multiplying the matrix on the right by an elementary matrix.

Elementary row operations on a matrix are equivalent to multiplying the matrix on the left by an elementary matrix.