Question

A matrix is invertible if and only if it is row equivalent to the identity matrix

Answer 1

Since each elementary matrix is invertible, it follows that will beinvertible if and only if is invertible.But is in RREF, so either has an all zerorow or is equal to the identity. Therefore is invertible if and only if it is the identity and will be non-invertible if and only if it has an all zero row.

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