Question

What is the determinant of a matrix used for?

Answer 1

The determinant of a matrix `A` helps you to find the inverse matrix `A^(-1)`.

You can know a few things with it :

• `A` is invertible if and only if `Det(A) != 0`.

• `Det(A^(-1)) = 1/(Det(A))`

• `A^(-1) = 1/(Det(A)) * ""^t((-1)^(i+j)*M_(ij))`,

where `t` means the transpose matrix of `((-1)^(i+j)*M_(ij))`,

where `i` is the n° of the line, `j` is the n° of the column of `A`,

where `(-1)^(i+j)` is the cofactor in the `i`-th row and `j`-th column of `A`,

and where `M_(ij)` is the minor in the `i`-th row and `j`-th column of `A`.