a) Show that the positive integers less than 11, except 1 and 10, can be split into pairs of integers such that each pair consists of integers that are inverses of each other modulo 11.________________b) Use part (a) to show that 10! = -1 (mod 11)

M303 Section 2.3 Notes- Characterizations of Invertible Matrices 10-14-16 Theorem 8- Invertible Matrix Theorem (IMT)- Let be × matrix; the following are equivalent: o is invertible o = o has pivot positions in its EF o = has only trivial solution o Columns of are linearly independent o LM :ℝ → ℝ given by = is 1-1 o = has a solution for all o Columns of span ℝ o LM :ℝ → ℝ given by = is onto o There exists an × matrix such that = o There exists an × matrix such that