Question

Prove that a matrix a in knxn is invertible if and only if the columns of a form a basis of kn

Answer 1

There's a linear algebra problem I'm having some trouble with:

Let A and B be square matrices with the dimensions n×n.

Prove or disprove:

If A2+BA is invertible, then A is also invertible.

If A2+BA is not invertible, then A isn't invertible either.

Any help with this would be appreciated. I recognize that if A2+BA is invertible then there is a matrix C so that (A2+BA)⋅C=I but beyond that I'm a little lost.

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