Thread: Help on a matter involving matrices and determinants

I have tried many ways to solve an issue, but I have not had a good success. The question is one that follows:

A is a matrix of order 3x3. B is a matrix of order 2X3

A=B^T*B (A is equal B transpose multiplied by B)

Calculate the determinant of A^2 for any matrix A of order 3X3 .

I tried to be as direct as possible. I thank you for your help!

"Caculate the determinant of A^2 for any matrix A of order 3X3" does not seem to have anything to do with "A= B^T*B".

Did you mean "Calculate the determinant of A^2 for any matrix A, of the form A= B^T*B for some matrix B, of order 3X3"?

It will help to know that $\displaystyle det(AB)=det(A)det(B)$, so that $\displaystyle det(A^2)= (det(A))^2$ and perhaps that $\displaystyle det(B^T)= det(B)$.

I agree, to calculate the determinant of A^2 for any matrix of order 3X3. However, A must be A=B^T*B e B is a matrix of order 2X3.