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# $$Does$$ $$it$$ $$exist ??$$

I came across a sum related to matrices which is as follows: $$A , B , C$$ are square matrices of order $$2 , 3 , 4$$ respectively. Also $$det(A)=2 , det(B)=3 , det(C)=4$$ then find $$det(ABC)$$.

$$(a)6$$ $$(b)12$$ $$(c)24$$ $$(d)does$$ $$not$$ $$exist$$. Solve the problem and also give reason for your answer.

Note by Akash Shah
2 years, 10 months ago

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Does not exist. The orders of all the matrices are different thus no two of the can be multiplied.. To elaborate A(m:n) B(p:q) AB exists if n=q BA exists if p=m Thus AB is not equal to BA · 2 years, 10 months ago

Well I too thought the answer as 'does not exist' but the answer was given 24.That's why to verify whether I was correct or not , I posted this note. · 2 years, 10 months ago

Of course, it does not exist as you cannot compute $$ABC$$, $$A$$,$$B$$,$$C$$ being matrices of different orders. · 2 years, 10 months ago