Parenthesis vs brackets for matrices
Solution 1:
It is just a question of notation and what you are comfortable with. The only thing you might want to be aware is |A| stands for determinant of the matrix A and hence cannot be used in place of () or [] to represent the matrix
Solution 2:
They're interchangeable. I think a lot of people tend to use parentheses just because they're easier to write by hand.
Solution 3:
There are two notations for matrices, ( ), [ ]. Use the one with which you are comfortable with.
Below are examples of both for the 3x3 Identity matrix.
$$
\begin{pmatrix}
1 & 0 & 0 \\
0 & 1 & 0 \\
0 & 0 & 1
\end{pmatrix}
\\
\begin{bmatrix}
1 & 0 & 0 \\
0 & 1 & 0 \\
0 & 0 & 1
\end{bmatrix}
$$
Solution 4:
This is a common questions that I've been asked time to time. Whether or not you choose to use:
\begin{pmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{pmatrix}
or
\begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix}
is up to you.
The difference between the notations is that the parenthesis notation \begin{pmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{pmatrix}
is mostly used by mathematicians.
However, the square bracket notation \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix} is mostly used by engineers or physicists (i.e. all other science disciplines other than mathematics). This is analogous to the reason why the spherical coordinate system used by physicists and engineers have the two angles labelled the other way, compared to that used by mathematicians. As a mathematician, I tend to stick with using the parenthesis notation.
Having said that, it is worth noting that | | notations denotes its determinant, not a matrix itself.