# given a square matrix A of order 3x3 such that |A| =12 then find the value of |A adjA|

A.adjA = adjA.A = |A|I

Therefore |A.adjA|can be find easily as,

|A.adjA|=||A|*I |

|A.adjA|=|A|

^{3}.| I |

|A.adjA|=12

^{3}.1=1728

using the determinant property that |cA|=(c^n)*|A| and n here is 3 and A=I