Can we use simultaneous row and column operations in solving same determinant? Please help.. Can both(row and column) operations be used simultaneously in finding the value of same determinant means in solving same question at a single time?
 A: A row operation corresponds to multiplying a matrix $A$ on the left by one of several elementary matrices whose determinants are easy to compute to get a matrix $B = EA$. For instance, swapping the rows of a 2x2 matrix is done with 
$$
\pmatrix{0 & 1 \\ 1 & 0 } \pmatrix{a & b \\ c & d}
$$
The determinant of the resulting row-swapped matrix is the product of the two determinants. Hence $det B = det E det A$. Since $det E = -1$ in this case, you can compute the det of the new matrix and multiply it be $-1$ to get the det of the original one. (This is typically not very useful, but it's an example). 
In the same way, a column op is done with $A \mapsto AE$, and you can use the same rule -- prduct of determinants -- to relate the determinant of $B = AE$ to the determinant of $A$. 
In short: you can do a sequence of row and column ops, each of which adds a factor to the determinant, until you reach the identity. You don't have to do just a sequence of row ops or just a sequence of column ops. 
Personal advice: Just use one or the other. It'll take a little longer, but you're much less likely to make a mistake in my experience with many students over the years. 
A: Remember that a set of row operations on a matrix $A$ can be represented by a matrix $P$
$$A^{\prime}=PA$$
Here $A^{\prime}$ is the matrix $A$ after the operations. In the same way, column operations are represented by a matrix $Q$ such that
$$A^{\prime}=AQ$$
After both row a column operations you have
$$A^{\prime}=PAQ$$
so
$$\det A^{\prime}=\det P\det Q\det A$$
Here $\det P$ and $\det Q$ are factors that depends on your exact operations: row addition (factor $1$), row transposition (factor $-1$) and row multiplication by $c$ (factor $c^{n}$, where $n\times n$ is the size of the matrices).
