$Does$ $it$ $exist ??$

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.

#Matrices

Easy Math Editor

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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

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 - 7 years ago

Of course, it does not exist as you cannot compute $ABC$ , $A$ , $B$ , $C$ being matrices of different orders.

Shaan Vaidya - 7 years 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.

Akash Shah - 7 years ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

DoesDoesDoes ititit exist??exist ??exist??

Comments

$Does$ $it$ $exist ??$