show that the matrix is the divisior of zero in M2(z)
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Step-by-step explanation:
The idea will work. But your BB is a vector, not a 2×22×2 matrix. Easy fix: let B∗B∗ be the 2×22×2 whose columns are each equal to your BB.
Remark: Consider the matrix
A=(acbd),A=(abcd),
where AA is not the zero-matrix. Suppose the determinant ad−bcad−bc is equal to 00. We cannot have all of aa, bb, cc, dd equal to 00. So either at least one of cc or dd is non-zero, or one of aa or bb is non-zero. We assume that cc and dd are not both 00, and let you take care of the case where they are, but aa and
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