Question

If $A^T$ and $B^T$ are transpose matrices of the square matrices$A$ and $B$ respectively then ${\left(AB\right)}^T$ is equal to

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

Answer 1

The correct option is D

$B^T{A}^T$

Find the value of ${\mathbf{\left(}\mathbf{A}\mathbf{B}\mathbf{\right)}}^{\mathbf{T}}$:

Given $A^T$ and $B^T$ are transpose matrices of the square matrices$A$ and $B$.

From the properties of matrices, we have

${\left(\mathrm{AB}\right)}^{\mathrm{T}}=B^T{A}^T$

Hence, the correct option is D.