Answer
See below
Work Step by Step
Let A be an arbitrary $4 \times 4$ matrix. By doing elementary row operations to see how change the value of $det(A)$, we can conjecture the followings:
(a) When two rows of a matrix are interchanged, the determinant changes sign.
(b) When one row is multiplied by a scalar A, the determinant of the resulting matrix is equal to the determinant of the original one times.
(c) The determinant remains unchanged when a multiple of any row of the matrix is added to a different row.
