Replacing a random ith row and column from a matrix

Question

Currently I am trying to delete a randomly-chosen $i^{th}$ row and column from a square $n \times n$ matrix $A$. So far I come up with the following code:

Drop[A, {RandomInteger[{1, 400}]}, {RandomInteger[{1, 400}]}]

The problem with this command is that the random integer for {i} is not the same as the random integer for {j}.

Is there a way of making them consistent, so that I drop the ith row and corresponding column while maintaining the randomness of selecting $i$?

And if the aim was to not delete the row and column entirely but to replace all their elements with, say 0, how would you go about it?

Thank you.

Answer 1

Perhaps either of these:

Drop[A, {#}, {#}]&@ RandomInteger[{1, Length@A}]
With[{i = RandomInteger[{1, Length@A}]}, Drop[A, {i}, {i}]]

Answer 2

A = Array[a, {7, 7}];

You can also use BlockRandom:

SeedRandom[123]
Drop[A, {BlockRandom[RandomInteger[{1, 7}]]}, {RandomInteger[{1, 7}]}] // MatrixForm

Alternatively,

SeedRandom[123]
Drop[A, {ri = RandomInteger[{1, 7}]}, {ri}] // MatrixForm