4 ms·
I'm confused: [42] is an invertible matrix with integer coefficients, right?
by abecedarius 10y ago
I'm confused: [42] is an invertible matrix with integer coefficients, right?
- taejo 10y agoI guess daniel-levin meant to say "invertible matrix with integer coefficients whose inverse also has invertible coefficients". The fact isn't too hard to see: * If M has integer coefficients, then det(M) is an integer. * det(inv(M)) = 1/det(M) * Since M has integer coefficients, det(M) is an integer * Since inv(M) has integer coefficients, det(inv(M)) is an integer * So det(M) and 1/det(M) are both integers, so det(M) is either 1 or -1
- taejo 10y agos/invertible coefficients/integer coefficients/
- sixo 10y agoYes, the claim is false. It's not obvious to me what it's been confused for. Edit: oh, the other commenter figured it out.