- #1

fluidistic

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## Homework Statement

I have the matrix A as being (-2 3 2; 6 0 3; 4 1 -1) and I'd like to calculate its determinant via calculating its cofactor matrix, even if I know it's much more laborious than just calculating its determinant.

I've calculated its cofactor matrix as being (-3 18 6; 5 -6 14; 9 18 -18). I've checked up the arithmetic twice and even redone all the arithmetic but I always fall over this cofactor matrix so I'm almost sure I didn't make any error.

Now from my notes in order to get the determinant, I must sum up all the entries of A multipled with their correspondant in the cofactor matrix.

That is, the arithmetic should start like : [tex](-2)\cdot (-3)+3\cdot 18 + 2\cdot 6[/tex]...

I finally get a result of 216 which is [tex]3 \times 72[/tex]. While calculating the determinant of A simply, I get 72. I'm sure I'm doing something wrong... and also I don't know if this factor 3 is a pure coincidence.

My question is : is it the right way to calculate the determinant of A, supposing that my cofactor matrix is right?