Hi all, I have encountered a contradiction which I cannot resolve by myself, so someone please help me out here:
we know that the formula for the inverse of a 2x2 A if A is [a b; c d] then the inverse of A is (1/(ad-bc)) * [d -b; -c a]
but from my textbook it says: det (A^-1) should = 1/(det(A)); because of:
det(A*A^-1) = det(I) = 1 = det(A) * det(A^-1) and that makes det(A^-1) = 1/det(A)
now if i was to use the 2x2 matrix as an example and do det(A), i get ad-bc, and det(A^-1) = det((1/(ad-bc)*[d -b; -c a]) is just 1! since you get (da-bc)/(ad-bc). That sure isn't right?

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ab
cd
inverse, isnt the inverse divided by the det?

it has to be 1

hard to parse your postings ... but i see where you have it

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