Matrices & Determinants Question - None

Question

If Δ =

|\begin{matrix} a_{1} & b_{1} & c_{1} \\ a_{2} & b_{2} & c_{2} \\ a_{3} & b_{3} & c_{3} \end{matrix}|

and A1, B1, C1 denote the co-factors of a1, b1, c1 respectively, then the value of the determinant

|\begin{matrix} A_{1} & B_{1} & C_{1} \\ A_{2} & B_{2} & C_{2} \\ A_{3} & B_{3} & C_{3} \end{matrix}|

is -

Accepted Answer

Let A be the matrix whose determinant is \Delta. The given determinant is the determinant of the cofactor matrix of A, which is adj(A^T). The determinant of the cofactor matrix is |adj(A)| = |A|^(n-1). Since n=3, the value is \Delta^(3-1) = \Delta^2.

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