question_answer 41)

Verify A(adj A) = (adj A) = |A| I for matrix

Answer:

|A| =       = 1(0 ? 0) + 1 (9 + 2) + (0 ? 0) = 11       A11 = (?1)1+1(0 ? 0) = 0;       A12 = (?1)1+2(9 + 2) = ?11;       A13 = (?1)1+3(0 ? 0) = 0;       A21 = (?1)2+1(?3 ? 0) = 3;       A22 = (?1)2+2(3 ? 2) = 1;       A23 = (?1)2+3(0 + 1) = ?1       A31 = (?1)3+1(2 ? 0) = 2;       A31 = (?1)3+2(?2 ? 6) = 8;       A33 = (?1)3+3(0 + 3) = 3                                              ?. (1)       and (adj A) A =             (adj A) A = 11       Also |A| I = 11       From (1), (2) and (3), we get       A(adj A) = (adj A) A = |A| I