Question

The value of the determinant of a matrix A of order 3 is 3. If C is the matrix of cofactors of the matrix A, then what is the value of the determinant of C²?

Answer 1

n = 3

|A| = 3

As per question,

C = (adj A)^T

∴ |C| = |(adj A)^T|

= |adj A|

∴ |C| = |A|^{n – 1}

= 3^{3 – 1}

= 3²

= 9

|C²| = |C| · |C|

= 9 × 9

= 81