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Math Help - Help with Linear Algebra proof

  1. #1
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    Help with Linear Algebra proof

    I've been brushing up on some linear algebra this summer, and came across this problem in a practice book. I'm totally stuck on how to do this!

    Prove that if M is an nxn matrix and can be written as

    M=\left(\begin{array}{cc}A&B\\0&C\end{array}\right  )

    where A and C are square matrices, then det(M) = det(A)*det(C).

    Anyone have a proof for this? I was almost wondering if I should try and use induction for n>=2 since this is true for a 2x2 matrix. Is there an easier (or more correct) way to prove this?
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  2. #2
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    Actually, I think it's a lot more simple than that!

    I just converted A and C into upper triangular matrices, which in turn makes M upper triangular, which means det(M) = det(A)*det(C). So simple!
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