Help me solve this question and please state how you arrived at the answer for learning purposes

Que 1

Suppose the fifth column of B is the sum of the first and last columns. What can be said about the fifth column of AB? VVhy? What can be said about the fifth column of AB? Why? 1:\" A. The fifth column of AB is the sum of the first and last columns of B. If B is [ b1 b2 bp ], then the fifth column of AB is Ab5 by definition. It is given that h5 = b1 + bp. By matrix-vector multiplication, Ab5 =(b1+bp) =b1+bp. The fifth column ofAB is the sum of the first and last columns ofAB. If B is [ b1 b2 bID ], then the fifth column of AB is Ab5 by definition. It is given that h5 = b1 bp. By matrix-vector multiplication, Ab5 =A(b1 bp)=Ab1 Abp. ' The fifth column ofAB is the sum of the first and last columns ofAB. If B is [ b1 b2 bIO ], then the fifth column of AB is Ab5 by definition. It is given that h5 = b1 + bp. By matrix-vector multiplication, Ab5 =A(b1+ bp)=Ab1+ Abp. The fifth column ofAB is the sum of the first and last columns of B. If B is [ b1 b2 bp ], then the fifth column of AB is Ab5 by definition. It is given that h5 = b1 - bp. By matrix-vector multiplication, Suppose A, B, and X are n x n matrices with A, X, and A - AX invertible, and suppose that (A - AX) " = X- B. Complete parts (a) and (b) below. . . . a. Explain why B is invertible. Choose the correct answer below. O A. Solving the equation (A - AX) - 1 =X- B for B yields (A - AX) " 'X =B. Since X is invertible and (A - AX) - is invertible, the product (A - AX) - 'X = B is also invertible. B. Solving the equation (A - AX) " = X- B for B yields X(A - AX) = B. Since X is invertible and (A - AX) ~ is invertible, the product X(A - AX) = B is also invertible. C. Multiply both sides of equation (A - AX) " = X-B by B- to obtain X-= (A- AX) " B. Now multiply both sides by (A - AX) to obtain the equation B- = (A - AX)X. Thus, the inverse of B exists and B must be invertible. O D. Since X- B is equal to (A - AX) and (A - AX) " is invertible, X B is also invertible. Since X - B is invertible and X is invertible, B must be invertible. b. Solve the equation (A - AX) = = X-B for X. X =