For matrices, a mulitplicative identity is a square matrix Xsuch XA = AX = A for any square matrix A. Prove that X must be theidentity matrix.
Prove that for any invertible matrix A, the inverse matrix mustbe unique. Hint: Assume that there are two inverses andthen show that they much in fact be the same matrix.
Prove Theorem which shows that Gauss-Jordan Elimination producesthe inverse matrix for any invertible matrix A. Your proof cannotuse elementary matrices (like the book’s proof does).
Prove that null(A) is a vector space.
Prove that col(A) is a vector space.
