Step 1 :Given the matrix $A=\left[\begin{array}{ll}-4 & 3 \\ -5 & 2\end{array}\right]$, we are asked to compute $-4 A$.
Step 2 :In matrix multiplication, each element of the matrix is multiplied by the scalar. So, we just need to multiply each element of the matrix A by -4.
Step 3 :Doing this, we get the matrix $\left[\begin{array}{ll}16 & -12 \\ 20 & -8\end{array}\right]$.
Step 4 :Final Answer: The result of $-4A$ is $\left[\begin{array}{ll}16 & -12 \\ 20 & -8\end{array}\right]$. So, the final answer is $\boxed{\left[\begin{array}{ll}16 & -12 \\ 20 & -8\end{array}\right]}$.