Question

Let A, B, C and D be n x n matrices having the inverse. If ACBD = In, then which of the followings is equal to C-¹ ? c) DBA d) A-¹D-¹B a) BAD b) BDA e) C-¹ may not be exist.

Let A, B, C and Dbe ( n times n ) matrices having the inverse. If ( A C B D=I_{n} ), then which of the followings is equal to ( Cᶜ¹ ) ? a) ( B A D )

Answer 1

To find C^-1 given ACBD = In, rearrange the equation as ACB = D^-1A^-1B^-1 and conclude that C^-1 = D^-1A^-1B^-1, which is option (d) A^-1D^-1B.

Step-by-step explanation:

To find C-1 given that ACBD = In, we can rearrange the equation as ACB = D-1A-1B-1. Therefore, C-1 = D-1A-1B-1, which is option (d) A-1D-1B.