证：由行列式按一行（列）展开公式k=id,akiA +ak2Ai2 +...+aknAin10,k+id =|Al.(d,l=jauA, +aA2, +.+ anAwj(0,l+j立即可得，Allania12aA21InAn2A12An2a22a2na21AA* =AinAzn ... Annanannan200d0d0同理，A*A=dE.= dE.00d..84.4矩阵的逆区区§4.4 矩阵的逆 证：由行列式按一行（列）展开公式 立即可得, 11 12 1 11 21 1 * 21 22 2 12 22 2 1 2 1 2 n n n n n n nn n n nn a a a A A A a a a A A A AA a a a A A A       =          d A = . 1 1 2 2  , 0, k i k i kn in d k i a A a A a A k i = + + + =  1 1 2 2  , 0, l j l j nl nj d l j a A a A a A l j = + + + =  0 0 0 0 . 0 0 d d dE d     = =       同理, * A A dE =