A,B都是三阶可逆矩阵,且|A|=2,|B|=3\2,则|(AB)*|=
问题描述:
A,B都是三阶可逆矩阵,且|A|=2,|B|=3\2,则|(AB)*|=
答
设C=AB
(AB)*=C*=|C|C^(-1)
|(AB)*|=|C|^3 * |C^(-1)|=|C|^3 * |C|^(-1)= |C|^2
而|C|=|AB|=|A| * |B|=3
所以|(AB)*|=3^2=9
答
|(AB)*|
= |AB|^(3-1)
= (|A||B|)^2
= 3 ^2
= 9