Question

If A, B, and C are invertible matrices, the expression (AB^-1)^-1(CA^-1)^-1C2 evaluates to ____________

(a) BC

(b) C^-1BC

(c) AB^-1

(d) C^-1B

I had been asked this question during an online exam.

This question is from Groups topic in section Groups of Discrete Mathematics

Answer 1

Correct answer is (a) BC

The explanation: Using the properties (AB)^-1=b^-1A^-1 and (A^-1)^-1=A, we may have,

(AB^-1)^-1(CA^-1)^-1C2

=(B^-1)^-1A^-1(A^-1)^-1C^-1C2

=BA^-1AC^-1C2

=BIC=BC [As, A^-1A=I].