Can I please have help with this question? Thanks

Exercise Exercise Exercise Exercise Exercise Exercise 54 55 56 57 58 59 Show that an m X n, matrix A has a right inverse iff rank(A) = m. Such a matrix is called a full row-rank matrix. Write down explicitly all right inverses of A. Hint: I just did it. Find all x that satisfy the equation xH A = bH explicitly in terms of the LU factorization of A {not AH). Show that an m X to. matrix A has a left inverse iff rank(A) = n. Such a matrix is called a full column-rank matrix. Write down explicitly all left inverses of A in terms of the LU decomposition of A [not AH). Show that if a matrix has both a left and right inverse then it is square. Show that A has a left inverse iff Ax = 0 implies x = 0. Show that A has a right inverse iff xH A = 0 implies x = 0