You must show that DC-1BA-1 when multiplied by AB-1CD-1 yields the Identity Matrix.
(DC^-1BA^-1)(AB^1CD^1)= I to prove product of expressions = I
(DC^-1B)(A^-1A)(B^1CD^1)= I Associative Law
(DC^-1B)(I)(B^1CD^1)= I Multiplicative Inverses
(DC^-1B)(B^1CD^1)= I Multiplicative Identity
(DC^-1)(BB^1)(CD^1)= I Associative Law
(DC^-1)(I)(CD^1)= I Multiplicative Inverses
(DC^-1)(CD^1)= I Multiplicative Identity
D(C^-1C)D^1= I Associative Law
D(I)D^-1= I Multiplicative Inverses DD^-1 = I Multiplicative Identity
I = I Multiplicative Inverses