Answer:
Option d.
Step-by-step explanation:
The given matrices are
[tex]A=\begin{bmatrix}3&2&-4\\ \:5&-5&-3\\ \:4&1&1\end{bmatrix}[/tex]
[tex]B=\begin{bmatrix}2&-4&1\\ \:5&-3&2\\ \:4&4&-5\end{bmatrix}[/tex]
We need to find BA.
[tex]BA=\begin{bmatrix}2&-4&1\\ \:5&-3&2\\ \:4&4&-5\end{bmatrix}\begin{bmatrix}3&2&-4\\ \:5&-5&-3\\ \:4&1&1\end{bmatrix}[/tex]
[tex]BA=\begin{bmatrix}2\cdot \:3+\left(-4\right)\cdot \:5+1\cdot \:4&2\cdot \:2+\left(-4\right)\left(-5\right)+1\cdot \:1&2\left(-4\right)+\left(-4\right)\left(-3\right)+1\cdot \:1\\ 5\cdot \:3+\left(-3\right)\cdot \:5+2\cdot \:4&5\cdot \:2+\left(-3\right)\left(-5\right)+2\cdot \:1&5\left(-4\right)+\left(-3\right)\left(-3\right)+2\cdot \:1\\ 4\cdot \:3+4\cdot \:5+\left(-5\right)\cdot \:4&4\cdot \:2+4\left(-5\right)+\left(-5\right)\cdot \:1&4\left(-4\right)+4\left(-3\right)+\left(-5\right)\cdot \:1\end{bmatrix}[/tex]
[tex]BA=\begin{bmatrix}-10&25&5\\ 8&27&-9\\ 12&-17&-33\end{bmatrix}[/tex]
Hence, option (d) is correct.
