(AB)^t=B^tA^t
게시글 주소: https://orbi.kr/00022414546
Let A be m×n and B be n×p then AB will be m×p (AB)^t will be p×m. for equation to hold it is necessary that right side be of identical dimension. since A^t is n×m B^t is p×n, the product B^tA^t is indeed p×m as required
(AB)^-1=B^-1A^-1
Let C be inverse matrix of AB then postmultiplication of C by AB will yield CAB that is same to I. i.e CAB=I. postmultiplication of both side by B^-1A^-1 will yield CABBA=BA but left side is reducible to CAA=CI=C thus C(inverse of A)=B^-1A^-1
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A^-1=adjA/|A|
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