I know that brackets are used to group variables and numbers together. Do brackets serve the same purpose when they are used with other 'objects' such as matrices or vectors?
For example, when brackets are used with matrices does this expression, $A(B+C)$ still mean multiply matrix $A$ with the matrix sum $B+C$?
On
As far as I know Yes.
The only times I have seen brackets behave differently depending on the field of math is for the specific examples below:
Geometry, where you can use them for points on a plane i.e. $(2, 1)$
Vectors, where you can display a vector as a position vector from the origin of a plane, allowing it to be expressed as a point as well i.e. $2i + 3j = (2,3)$ or it can be displayed as $2\choose3$
Complex Numbers, for yet again displaying a complex number as a point/position vector on the argand plane so e.g. $2 + 3i = (2,3)$
Matrices, when showing a matrix $\begin{bmatrix}a&b\\c&d\end{bmatrix}$, note that curly brackets still mean the same thing so $A(B+C) = AB + AC$
Combinatorics for choosing i.e. $3\choose2$ $= \frac{3!}{2!(3-2)!} = 3$
Functions, for passing the input i.e. $f(2)$ means input $x=2$ into the function $f(x)$ and not times the variable $f$ by $2$, note as well that this notation of putting the number in the bracket after the function also covers how $\mathrm{sin}(2) \neq 2\mathrm{sin}$ as instead of multiplication, the former means to pass the number $2$ to the sine function.
And set notation, so when creating a set you use curly brackets ${}$ so $N = \{2, 4, 6, 8, ...\}$ creates a set of all even numbers and not some infinite dimensional point
Yes, absolutely! They always are meant to force a certain order of operation, i.e they always do what is in the brackets first.