For the following, show that does not form a vector space over under the (non standard) operations (addition) and (multiplication).
(a)
(b)
multiplication by scalar is obviously not linear.
the additive inverse doesn't always exist! see that the additive identity, namely 0, here is the matrix with all entries equal 1. now let be the matrix with 0 in the first row and first column and(b)
whatever you want everywhere else. then has no additive inverse.