×

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

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, 8 months ago

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold
- bulleted- list
• bulleted
• list
1. numbered2. list
1. numbered
2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears 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} $$\boxed{123}$$

Sort by:

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

- 3 years, 8 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.

- 3 years, 8 months ago

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

- 3 years, 8 months ago