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If A and B are squares matrices such that A^2006=0 and AB=A+B,then find det(B).

Shivan Bhatt , 8 Years ago
Grade 12
anser 1 Answers
mycroft holmes

Last Activity: 8 Years ago

We have det A = 0. Also from A+B = AB we have B = AB-A = AB – AI = A(B-I)
 
so det B = det A det(B-I) = 0

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