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 __________.

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Solution

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

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 = BA. Here, B is the inverse of of matrix A.

However, in applying one or more row operations on A = IA while finding A^–1 by elementary row operations, if we obtain all zeroes in one or more row of the matrix A on the LHS, then the inverse of matrix A would not exist as we will not get I = BA 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.

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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 __________.

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 __________.