Step 1: Write all the elements of the array.
The given 2D array is:
\[
\begin{bmatrix}
4 & 5 \\
7 & 2 \\
19 & 4\\
7 & 43
\end{bmatrix}
\]
Step 2: Find the maximum element.
Now compare all the elements:
\[
4,\ 5,\ 7,\ 2,\ 19,\ 4,\ 7,\ 43
\]
The greatest value among these is:
\[
43
\]
Step 3: Find the minimum element.
The smallest value in the array is:
\[
2
\]
Step 4: Find the index of the minimum element.
In Java, array indexing starts from \(0\).
The element \(2\) is present in the second row and second column, so its index is:
\[
[1][1]
\]
Step 5: State the final answer.
Therefore:
\[
\boxed{\text{Maximum element} = 43}
\]
and
\[
\boxed{\text{Index of minimum element} = [1][1]}
\]