Recall that an nxn matrix is called skew-symmetric if A^T=-A. a)Prove that for all x that are in R^n we have x^TAx=0 (note: x^T Ax is a scalar for any nxn matrix A) b) Prove that I+A is invertible
My professor assigned a bunch of questions prior to our exam and I feel as though they haven't been adequately covered throughout the semester. I would really appreciate the help.
Hint: the fact that you know something about the transpose of $A$ suggests that taking the transpose of something in the problem will be productive.