**Question:**

In applying one or more row operations while finding $A^{-1}$ by elementary row operations, we obtain all zeroes in one or more row, then $A^{-1}$

**Solution:**

Let $A$ be a square matrix. In order to find the inverse of matrix $A$ using elementary row operations, we write $A=I A$.

Now, perform a sequence of elementary row operations successively on $A$ on the LHS and the pre-factor $I$ on RHS, till we get $I=B A$. Here, $B$ is the inverse of of matrix $A$.

However, in applying one or more row operations on $A=I A$ while finding $A^{-1}$ by elementary row operations, if we obtain all zeroes in one or more row of the matrix $A$ on the $L H S$, then the inverse of matrix $A$ would not exist as we will not get $/=B A$ in this case.

In applying one or more row operations while finding $A^{-1}$ by elementary row operations, we obtain all zeroes in one or more row, then $A^{-1}$ does not exist_.