设a是n阶矩阵,adja是a的转置伴随阵,若deta=5,求det[(5adja)-1]的值

问题描述:

设a是n阶矩阵,adja是a的转置伴随阵,若deta=5,求det[(5adja)-1]的值

|(5A*)^-1|
= |(1/5) A*^-1|
= |(1/5) (1/|A|)A|
= |(1/25)A|
= (1/25)^n |A|
= 5 /25^n
= 1/5^(2n-1)