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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
3 years 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 Ishan Bhatt · 3 years ago

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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. Akash Shah · 3 years ago

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Of course, it does not exist as you cannot compute \(ABC\), \(A\),\(B\),\(C\) being matrices of different orders. Shaan Vaidya · 3 years ago

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