Question

1.设A,B,C均为n阶可逆矩阵,则（ACB^T）^-1= 2.设A,B均为n阶可逆矩阵,/A/=5,则/B^-1A^k

Answer 1

（ACB^T）^-1= (B^T)^-1C^-1A^-1 = (B^-1)^TC^-1A^-12.|B^-1A^kB| = |B^-1| |A^k| |B| = |B|^-1 |A|^k |B| = |A|^k = 5^k3.A+B^-1 先左边提A,再右边提B^-1= A(E+A^-1B^-1)= A(B+A^-1)B^-1