b) To prove: (AB)^T = B^TA^T

Clearly, LHS = (AB)^T =

First multiplying the matrix and then taking the transpose.

∴ LHS =

⇒ LHS =

∴ LHS =

As RHS = B^TA^T

We will first take transpose of matrices and then multiply

RHS =

⇒ RHS =

Clearly, LHS = RHS =

Hence (AB)^T = B^TA^T …proved