Introductory Econometrics: A Modern Approach 6th Edition by Jeffrey M Wooldridge

Exercise 5

(i) Use the definition of inverse to prove the following: if A and B are n x n nonsingular matrices, then (AB)-1 = B-1A-1.

(ii) If A, B, and C are all n x n nonsingular matrices, find (ABC)-1 in terms of A-1, B-1, and C-1.

Step 1 of 4

A matrix ‘X’ of order ‘n×n’ is said to be invertible, if and only if these two conditions are satisfied:

Thus, ‘X’ is invertible or non-singular, if these conditions are fulfilled. Otherwise, it is called “non-invertible” or singular.