solution: A= 1 1 0 4 3 1 2 0 5 Finding the determinant of the matrix ? det A = -3 The determinant of A is non-zero, hence the inverse matrix A-1 exists. To find the inverse matrix was calculated the minors and cofactors of the matrix ? M1,1 = 3 1 0 5 = 15 C1,1 = (-1)1+1M1,1 = 15 M1,2 = 4 1 2 5 = 18 C1,2 = (-1)1+2M1,2 = -18 M1,3 = 4 3 2 0 = -6 C1,3 = (-1)1+3M1,3 = -6 M2,1 = 1 0 0 5 = 5 C2,1 = (-1)2+1M2,1 = -5 M2,2 = 1 0 2 5 = 5 C2,2 = (-1)2+2M2,2 = 5 M2,3 = 1 1 2 0 = -2 C2,3 = (-1)2+3M2,3 = 2 M3,1 = 1 0 3 1 = 1 C3,1 = (-1)3+1M3,1 = 1 M3,2 = 1 0 4 1 = 1 C3,2 = (-1)3+2M3,2 = -1 M3,3 = 1 1 4 3 = -1 C3,3 = (-1)3+3M3,3 = -1 Matrix of cofactors: C = 15 -18 -6 -5 5 2 1 -1 -1 Transpose of cofactor matrix: CT = 15 -5 1 -18 5 -1 -6 2 -1 Finding the inverse matrix. A-1 = CT = det A -5 5/3 -1/3 6 -5/3 1/3 2 -2/3 1/3 B) First, let\'s add the Identity Matrix to the right of our matrix 1 1 0 1 0 0 4 3 1 0 1 0 2 0 5 0 0 1 Now, let\'s do Gauss-Jordan Elimination on our new matrix... Add (-4 * row1) to row2 1 1 0 1 0 0 0 -1 1 -4 1 0 2 0 5 0 0 1 Add (-2 * row1) to row3 1 1 0 1 0 0 0 -1 1 -4 1 0 0 -2 5 -2 0 1 Divide row2 by -1 1 1 0 1 0 0 0 1 -1 4 -1 0 0 -2 5 -2 0 1 Add (2 * row2) to row3 1 1 0 1 0 0 0 1 -1 4 -1 0 0 0 3 6 -2 1 Divide row3 by 3 1 1 0 1 0 0 0 1 -1 4 -1 0 0 0 1 2 -2/3 1/3 Add (1 * row3) to row2 1 1 0 1 0 0 0 1 0 6 -5/3 1/3 0 0 1 2 -2/3 1/3 Add (-1 * row2) to row1 1 0 0 -5 5/3 -1/3 0 1 0 6 -5/3 1/3 0 0 1 2 -2/3 1/3 The inverse matrix can now be found in the right 3 columns of our reduced row echelon matrix Here is the inverse matrix: -5 5/3 -1/3 6 -5/3 1/3 2 -2/3 1/3 A= 1 1 0 4 3 1 2 0 5 Solution solution: A= 1 1 0 4 3 1 2 0 5 Finding the determinant of the matrix ? det A = -3 The determinant of A is non-zero, hence the inverse matrix A-1 exists. To find the inverse matrix was calculated the minors and cofactors of the matrix ? M1,1 = 3 1 0 5 = 15 C1,1 = (-1)1+1M1,1 = 15 M1,2 = 4 1 2 5 = 18 C1,2 = (-1)1+2M1,2 = -18 M1,3 = 4 3 2 0 = -6 C1,3 = (-1)1+3M1,3 = -6 M2,1 = 1 0 0 5 = 5 C2,1 = (-1)2+1M2,1 = -5 M2,2 = 1 0 2 5 = 5 C2,2 = (-1)2+2M2,2 = 5 M2,3 = 1 1 2 0 = -2 C2,3 = (-1)2+3M2,3 = 2 M3,1 = 1 0 3 1 = 1 C3,1 = (-1)3+1M3,1 = 1 M3,2 = 1 0 4 1 = 1 C3,2 = (-1)3+2M3,2 = -1 M3,3 = 1 1 4 3 = -1 C3,3 = (-1)3+3M3,3 = -1 Matrix of cofactors: C = 15 -18 -6 -5 5 2 1 -1 -1 Transpose of cofactor matrix: CT = 15 -5 1 -18 5 -1 -6 2 -1 Finding the inverse matrix. A-1 = CT = det A -5 5/3 -1/3 6 -5/3 1/3 2 -2/3 1/3 B) First, let\'s add the Identity Matrix to the right of our matrix 1 1 0 1 0 0 4 3 1 0 1 0 2 0 5 0 0 1 Now, let\'s do Gauss-Jordan Elimination on our new matrix... Add (-4 * row1) to row2 1 1 0 1 0 0 0 -1 1 -4 1 0 2 0 5 0 0 1 Add (-2 * row1) to row3 1 1 0 1 0 0 0 -1 1 -4 1 0 0 -2 5 -2 0 1 Divide row2 by -1 1 1 0 1 0 0 0 1 -1 4 -1 0 0 -2 5 -2 0 1 Add (2 * row2) to row3 1 1 0 1 0 0 0 1 -1 4 -1 0 0 0 3 6 -2 1 Divide row3 by 3 1 1 0 1 0 0 0 1 -1 4 -1 0 0 0 1 2 -2/3 1/3 Add (1 * row3) to row2 1 1 0 1 0 0 0 1 0 6 -5/3 1/3 0 0 1 2 -2/3 1/3 Add (-1 * row2) to row1 1.