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Question

Let $$A = \left[ {\matrix{ 1 & { - 2} & \alpha \cr \alpha & 2 & { - 1} \cr } } \right]$ and $B = \left[ {\matrix{ 2 & \alpha \cr { - 1} & 2 \cr 4 & { - 5} \cr } } \right],\,\alpha \in C$. Then the absolute value of the sum of all values of $\alpha$$ for which det(AB) = 0 is :

3
4
2
5

Solution

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