Highlight the Bounding Box, Part I: Cartesian Grid You're given a rectangular grid of the characters . and #, like this:
..........
..#.......
....#..#..
...#......
..........

Your task is to fill the entire axis-aligned bounding box of the # with further #:
..........
..######..
..######..
..######..
..........

The axis-aligned bounding box is the smallest rectangle which contains all the #.
Want more? Try Part II!
Rules
You may use any two distinct printable ASCII characters (0x20 to 0x7E, inclusive), in place of # and .. I'll continue referring to them as # and . for the remainder of the specification though.
Input and output may either be a single linefeed-separated string or a list of strings (one for each line), but the format has to be consistent.
You may assume that the input contains at least one # and all lines are the same length.
You may write a program or a function and use any of the our standard methods of receiving input and providing output.
You may use any programming language, but note that these loopholes are forbidden by default.
This is code-golf, so the shortest valid answer – measured in bytes – wins.
Test Cases
Each test case has input and output next to each other.
#    #

...    ...
#..    #..
...    ...

...    ...
#..    ###
..#    ###

.#.    ###
#..    ###
..#    ###

.....    .....
.#.#.    .###.
.....    .....

...    ...
.#.    .#.
...    .#.
.#.    .#.
...    ...

..........    ..........
..........    ..........
....#.....    ....#.....
..........    ..........

..........    ..........
..........    ..........
....#.....    ...##.....
...#......    ...##.....

..........    ..........
..#.......    ..###.....
....#.....    ..###.....
...#......    ..###.....

..........    ..........
..#.......    ..######..
....#..#..    ..######..
...#......    ..######..

.........#    ..########
..#.......    ..########
....#..#..    ..########
...#......    ..########
VBA Excel, 150 bytes 146 bytes

Instruction:

Create a workbook with two blank worksheets: Sheet1 and Sheet2. Set the input in Sheet1 and then put the following code in the Sheet1 code module

Sub A:For Each C In UsedRange:If C.Value="#"Then Sheet2.Range(C.Address)="#"
Next:For Each C In Sheet2.UsedRange:Range(C.Address)="#":Next:End Sub


Ungolfed the code:

Sub A()

For Each C In UsedRange
    If C.Value = "#" Then Sheet2.Range(C.Address) = "#"
Next

For Each C In Sheet2.UsedRange
    Range(C.Address) = "#"
Next

End Sub


Explanation:


Loop through every cell in the used range Sheet1
Set the conditional statement to copy every cell contains character hashtag (#) in the used range Sheet1 and paste it to the cell in Sheet2 with the same address as Sheet1.
Loop through once again every cell in the used range Sheet2 to copy every cell address in it and then use it to assign character hashtag (#) to the cell in Sheet1 with the same address as the used range Sheet2.


Example I/O:

  



Caveat: Make sure every cell in Sheet2 always blank every time you run the program.