Thread: What is the dimension of M(2x2) over K? Find basis? (linear algebra)

M(2x2)(R) is a vector space of K.
M =
(a......b)
(-b.....a)

one way of thinking of a basis is it tells us: "how many pieces of information we need to specify". how many numbers (scalars) do you have to know to completely determine the matrix:

?

can you write the matrix as:

a*something + b*(another something)?

what might the "somethings" be?