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Properties of the determinant

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1. I'm stuck on b.. and not entirely sure of a either. I'll upload my working later but if someone could give me a few pointers I'd appreciate it.. like which properties I should use etc.
2. (Original post by StarvingAutist)

I'm stuck on b.. and not entirely sure of a either. I'll upload my working later but if someone could give me a few pointers I'd appreciate it.. like which properties I should use etc.
For a), I think that you need to consider expanding the determinant in terms of the column. The dot product with is then equivalent to the determinant which is 0. (My notation looks a bit screwy, but I think that makes sense...)

For b) I can't quite get it clear in my head, but I think that you need to use the property that obtains when you multiply a row of a determinant by a scalar i.e. obtain B from A by that elementary row operation and you have

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