Augment the matrix with the identity matrix on the right. Then do row operations to get the identity on the left, and the inverse will be on the right:----------------------------------------------- Swap rows 1 and 2 to get a non-zero element in the upper left corner: ----------------------------------------------- We get column 1 so that all its elements are 0 except the element in row 1. The least common multiple of the non-zero elements in column 1 is 2, so we get all the non-zero elements in column 1 to be 2 except row 1, and we get it to be -2 So we only need to multiply row 1 by -2 Add row 1 to rows 3 and 4, and restore row 1: ----------------------------------------------- We get column 2 so that all its elements are 0 except the element in row 2. The least common multiple of the non-zero elements in column 2 is 1, so we get all the non-zero elements in column 2 to be 1 except row 2, and we get it to be -1 So we only need to multiply row 2 by -1 Add row 2 to rows 1 and 4, and restore row 2: ----------------------------------------------- We get column 3 so that all its elements are 0 except the element in row 3. The least common multiple of the non-zero elements in column 3 is 6, so we get all the non-zero elements in column 3 to be 6 except row 3, and we get it to be -6 So we need to multiply row 2 by 3 multiply row 3 by 3 multiply row 4 by -2 Add row 3 to rows 2 and 4, and restore row 3 ----------------------------------------------- We get column 4 so that all its elements are 0 except the element in row 4. The least common multiple of the non-zero elements in column 4 is 3, so we get all the non-zero elements in column 4 to be 3 except in row 4, and we get it to be -3 So we need to multiply row 1 by 3 multiply row 2 by -1 multiply row 3 by -1 multiply row 4 by -3 Add row 4 to rows 1, 2, and 3, and restore row 4 Get 1's on the diagonal Divide row 1 by 3 Divide row 2 by -3 Divide row 3 by 2 ------------------------------------- Now that we have the identity matrix on the left of the petition, the inverse of the given matrix is the 4×4 matrix on the right of the petition: Edwin