GATE CS 1997 Q4.2 — Linear Algebra: Matrices, Determinants, System of Linear Equations

When we multiply a matrix $A$ on the right by an elementary matrix $E$ (i.e., $AE$), it performs the corresponding column operation on $A$:

• The matrix $I_{12}$ is obtained by interchanging the first and second rows (or equivalently, the first and second columns) of the identity matrix $I$.
• Post-multiplying $A$ by $I_{12}$ to form $AI_{12}$ interchanges the first and second columns of $A$.

Therefore, the first column of the resulting matrix $AI_{12}$ is identical to the second column of $A$, and the second column of $AI_{12}$ is identical to the first column of $A$. This matches option C.