1. The problem statement, all variables and given/known data Find the inverse of matrix A 02 30 3. The attempt at a solution I was thinking of doing a row swap to get a diagonal matrix with nonzero diagonal entries, PA (a.k.a. B). I want this matrix's inverse, B-inverse (easily found by dividing the ones of the identity matrix by the diagonal entries) to serve as a means to get to A-inverse I want to use this relationship specifically: (B-inverse)(PA)=(A-inverse)(A)=I. I want to multiply all sides by A-inverse to show that (B-inverse)(P)=(A-inverse), but I am really shaky as to how I properly utilize the multiplication rules for matrices in this case. For example: Would multiplying both sides by A-inverse cancel out A? Wouldn't I be applying A-inverse to the outermost matrix and not even hit A? To sum: Where I really get lost is how to properly manipulate matrix equations in order to cancel. Let me know if you have any questions. Sorry I couldn't make the post more visual. Don't know how to draw out matrices.