" 1) Let A be a 3 x 3 matrix with determinant 4. Then det(adj(A^T)) = ?, det(adj(A^-1)) = ? and det(adj(4A)) = ?.
2) Let A be a 2 x 2 matrix such that adj(A) = \begin{pmatrix}-5&-1\\ 3&6\end{pmatrix}
Then det A = ?"
I am a little confused as to how I am supposed to link ad joints, determinants and matrix transposes together. Are there any rules to do this? Also, how would I calculate the transpose of a matrix just by being given its dimensions and determinant. And finally, how would I calculate the determinant of a matrix given its ad joint. This was also something that confused me.
Any assistance would be highly appreciated!
2) Let A be a 2 x 2 matrix such that adj(A) = \begin{pmatrix}-5&-1\\ 3&6\end{pmatrix}
Then det A = ?"
I am a little confused as to how I am supposed to link ad joints, determinants and matrix transposes together. Are there any rules to do this? Also, how would I calculate the transpose of a matrix just by being given its dimensions and determinant. And finally, how would I calculate the determinant of a matrix given its ad joint. This was also something that confused me.
Any assistance would be highly appreciated!