Which of the following statements is false? O If the matrix product AC is equal to the identity matrix, then A is invertible. O If the columns of a square matrix are linearly independent, then the matrix is invertible. O If the transpose of A is invertible, then A is invertible. If A is an n-by-n matrix and has a pivot in every column, then A is invertible.The invertible matrix theorem lists many statements that are equivalent. lf one of the statements is false. then all of the other statements are false. On the other hand. if one of the statements is true. all the other statements are true. Notice that the only hypothesis or condition on the theorem is that the matrix is square. 1. If A is an n x 11 matrix with n pivots, explain why Ax = 0 has only the trivial solution. This shows that part (c) of the invertible matrix theorem implies that part [d] is true. 2. If A is invertible, then AT is invertible. Which theorem from section 2.2 says that this is true? This shows that it part (a) is true, then part (I) is true in the invertible matrix theorem. 3. Choose two other parts of the inverb'ble matrix theorem. Assume that one of the parts is true, and explain whyr it means that the other part is true