Which matrix is the inverse of matrix p

Connect and share knowledge within a single location that is structured and easy to search. I would appreciate it if somebody can help me. There are really three possible issues here, so I'm going to try to deal with the question comprehensively. First, since most others are assuming this, I will start with the definition of an inverse matrix. This definition says "an inverse" and not "the inverse. We could prove one or more of the following statements:.

This is proved directly from the definition. That is the proof. You seem to be concerned that you don't know how to begin, proving this from the definition of inverse, but that's literally all there is to it. You're just parsing the definition, applying a very simple property of equality, and then parsing the definition again to draw a slightly different conclusion.

It is foolhardy to assume that a more complicated proof is better here, especially one that relies on lemmas and properties that are themselves not axioms or definitions. That's just good practice, but in fact, it might be worse than that. It is also assuming inverses are unique, which is not necessary, see part 2 below. It is like the inverse we got before, but Transposed rows and columns swapped over.

We cannot go any further! This matrix has no Inverse. Such a matrix is called "Singular", which only happens when the determinant is zero. And it makes sense There needs to be something to set them apart. Well … how do we do that? Question LinAlgError : print 'Oops, looks like A is singular! Oops, looks like A is singular! A is row equivalent to the identity matrix. Follows directly from the previous statement. Follows directly the previous statement and the definition of linear independence.

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