Question 11 2 pts Let A and B be square matrices of the same dimension, and I be the identity matrix having the same dimension as A and B. If AB = 1 =BA, then ? O B is the inverse of A O A = B and B = A-1 O A is the inverse of B O all of the above are correctD Question 12 2 pts Suppose that A is a nonsingular matrix. Then which of the following is true? You may use a known nonsingular matrix example we used in class to verify which of the following is true. Manual computations or Matlab screenshot is needed for this question. O (AT) 1 = (A - 1)=1 O (AT) T = ( A - 1) T O (AT) - 1 = (A - 1) T O (AT)T = (A2)TD Question 13 2 pts True or False? If always true, choose true. Otherwise, choose false. Let A be an invertible matrix. Then, AB = AC implies B=C. O True O False D Question 14 2 pts Suppose A and B are square matrices of the same dimension. Which of the following is true? O det(A + B) = det(A) + det(B) O det(AT + A) = detAT) det(A) O det(AB)=det(B) det(A) none of the above is trueD Question 15 2 pts Suppose we have a square matrix A. Which of the following is false? O. None of the above is false. O Swapping row number 1 with row number 2 and then swapping row number 3 with row number 4 does not change the value of the determinant. O Swapping two rows in A results in a change of the sign of the corresponding determinant. . O Subtracting column number 2 from column number 1 does not alter the value of the determinant