How to change state space from higher dimension to lower?

I found the below text in a textbook. Can someone help in derivation

[Mario Malic]

I am not sure if this is the space for such questions.

But you know a rule of matrix multiplication such as A*A^(-1)= I and it matters from which side you do the multiplication. Should be enough to start something.

[Waqar Ahmed]

Actually these are the state space realizations matrices of transfer function. H(s)=C*(s*E-A)^-1*B+D. The transfer function is needed to derive these expressions