Expansion along first Row R 11 Step 1 Multiply first element a of R by 1 1 1 sum of suffixes in a11 and with the second order determinant obtained by deleting the elements of first row R and first column C of A as a lies in R and C i e 922 923 1 a 932 A33 Step 2 Multiply 2nd element a of R by 1 2 1 sum of suffixes in a order determinant obtained by deleting elements of first row R and 2nd column C of A as a 12 lies in R and C i e 1 2 a 2 Step 3 Multiply third element a 3 of R by 1 3 1 sum of suffixes in a and the second order determinant obtained by deleting elements of first row R and third column C of A as a 3 lies in R and C3 or 1 3a13 250 1951 i e Step 4 Now the expansion of determinant of A that is A written as sum of all three terms obtained in steps 1 2 and 3 above is given by 145 a31 932 922 a23 1 det A A 1 32 33 1 3 a a21 922 931 932 A a a22 a33 a32a23 12 a 1 a33 a31a23 a13 a 1 a32 931 922 a13 a 1 a22 A33 11 a 13 a31 a22 Note We shall apply all four steps together Expansion along second row R Expanding along R we get A 1 1 a Rationalised 2023 24 a11 a32a23 a 12 a21 a 33 a11 A a21 a 31 923 921 a32 A33 1 a12 a13 1 all a31 912 1 3 a21 a12 a33 a32 a 13 a22 a23 a11 a32 a31 9 2 a12 932 a 1 2 912 923 931 933 a13 22 23 a32 a33 RT 922 aus de 912 and the second all a13 a31 DETERMINANTS 79 a12 a31 a23 a13 a21 a32 a31 a 13 1 published