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So I have a question which says the following

(a) Given $A= \begin{bmatrix} 3 & 0 \\ -1 & 2 \\ 1 & 1 \end{bmatrix} $, $B= \begin{bmatrix} 4 &-1 \\ 0 & 2 \\ \end{bmatrix} $, $C= \begin{bmatrix} 1 & 4 & 2 \\ 3 & 1 & 5 \\ \end{bmatrix} $. Compute $(BA^T-2C)^T$.

If I use Transpose properties, I get $(B^TA-2C^T)$

But if I transpose $B$, the rows of $B$ and the columns of $A$ don't agree so I can't do the matrix multiplication so I can't compute the matrix. Did I do the matrix properties properly? Or is there a mistake in the question?

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    In general $(AB)^T=B^TA^T$, not $A^TB^T$. – 2017-02-03

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Using $(A.B)^{T} = B^{T}.A^{T}$. Now$(B . A^{T} - 2C)^{T} = (B . A^{T})^{T} - 2C^{T} = A.B^{T} - 2C^{T}$.

As you can see that matrix dimension of $A $ is $3$ by $2$ , $B^{T} $ is $2$ by $2 $ so dimension of $A.B^{T} $ is $3$ by $2$ and $C^{T}$ is of size $3$ by $2$,thus we can subtract .