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## Homework Statement

The set K of 2 × 2 real matrices of the form [a b, -b a] form a field with the usual operations.

It should be clear to you that M

_{22}(R) is a vector space over K. What is the dimension of M

_{22}(R) over K? Justify your answer by displaying a basis and proving that the set displayed is actually a basis.

## Homework Equations

## The Attempt at a Solution

I don't think there can be a basis over the field K, because no linear combination of the matrices [a b, -b a] with any M

_{22}can form, say [1 0, 0 0]. Which would be in M

_{22}. Any help would be greatly appreciated. Thanks!