(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let A be an invertible 3x3 matrix. Suppose it is known that:

A =

[u v w

3 3 -2

x y z]

and that adj(A) =

[a 3 b

-1 1 2

c -2 d]

Find det(A)

(answer without any unknown variables)

2. Relevant equations

3. The attempt at a solution

I found A^(-1) to be equal to

(1/det(A)) * adj(A)

So, then re-arranging the formula;

I*det(A) = A*adj(A)

So then det(A) =

[u v w

3 3 -2

x y z]

*

[a 3 b

-1 1 2

c -2 d]

I know the solution to this problem is det(A) = 16. Therefore it must be that

[3 3 -2] * [3 1 2] = det(A)

But, what I am confused about is:

Why is the det equal only to the position (2,2) of the matrix A*adj(A)? As the solution is taken as the position a_(2,2)...

Thanks!

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# Homework Help: Inverse Matrix Question

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