`color{green} ✍️` To every square matrix `A = [a_(ij)]` of order `n,` we can associate a number (real or complex) called determinant of the square matrix A, where `a_(ij) = (i, j)^(th)` element of A.
Determinant of a matrix of order one :
`A = [a ]` be the matrix of order 1, then determinant of A is defined to be equal to `color{orange}{|A| = a}`
Determinant of a matrix of order `2 × 2 : `
`=>` If `A = [(a_(11), a_(12)),(a_(21), a_(22))]` be a matrix of order 2 × 2,
then the determinant of A is defined as `color{orange}{|A| = |(a_(11), a_(12)),(a_(21), a_(22))|}`
Determinant of a matrix of order `3 × 3 : `
`color{green} ✍️` If `A = [(a_(11), a_(12),a_13),(a_(21), a_(22),a_23),(a_31,a_32,a_33)]` be a matrix of order `3 × 3, `
then the determinant of `A` is defined as `color{orange} |A| = |(a_(11), a_(12),a_13),(a_(21), a_(22),a_23),(a_31,a_32,a_33)| `
`color{green} ✍️` To every square matrix `A = [a_(ij)]` of order `n,` we can associate a number (real or complex) called determinant of the square matrix A, where `a_(ij) = (i, j)^(th)` element of A.
Determinant of a matrix of order one :
`A = [a ]` be the matrix of order 1, then determinant of A is defined to be equal to `color{orange}{|A| = a}`
Determinant of a matrix of order `2 × 2 : `
`=>` If `A = [(a_(11), a_(12)),(a_(21), a_(22))]` be a matrix of order 2 × 2,
then the determinant of A is defined as `color{orange}{|A| = |(a_(11), a_(12)),(a_(21), a_(22))|}`
Determinant of a matrix of order `3 × 3 : `
`color{green} ✍️` If `A = [(a_(11), a_(12),a_13),(a_(21), a_(22),a_23),(a_31,a_32,a_33)]` be a matrix of order `3 × 3, `
then the determinant of `A` is defined as `color{orange} |A| = |(a_(11), a_(12),a_13),(a_(21), a_(22),a_23),(a_31,a_32,a_33)| `