Question

Which among the following would be obtained on simplifying the expression $(A^{T}BA{)}^T$.

• A. $A^T{B}^T{A}^T$
• B. $A^T{B}^{T}A$
• C. $A{A}^T{B}^T$
• D. $B^T{A}^{T}A$

Answer 1

The correct option is B $A^T{B}^{T}A$

The main principle that has to be applied is, $(XY{)}^T=Y^T.X^T.$ Using this in our present case,
$(A^{T}BA{)}^T=(BA{)}^T.(A^T{)}^T$
$=A^T{B}^{T}A$
Note that in the first step we group the terms in the expression to $A^T$ and BA to apply this law.