**Properties of Inverse Matrices**

-1 If A and B are invertible matrices of the same order, then (i) (A-1)-1 = A (i) (AB)-1 = B-1 A-1 (iii) (Ak)-1 = (A-1)k, ke N (iv) adj (A-1)=(adj A) 1 (v)|A-113 1 =|A|-1 |A| -1

Note If A is an invertible matrix, then • If A is symmetric matrix, then A-' is also symmetric matrix, • If A is skew-symmetric matrix, then A-t is also skew symmetric matrix.