If │A│=3 and A^{-1} = ((3,-1),(-5/2,2/3)) then adj A = ? ​

Question

If │A│=3 and A^-1 = \(\begin{pmatrix}3&-1 \\-5/ 3 &2/3\end{pmatrix}\)then adj A = ?

A. \(\begin{pmatrix} 9&3 \\ -5 &-2 \end{pmatrix}\)

B.\(\begin{pmatrix} 9&-3 \\ -5 &2 \end{pmatrix}\)

C.\(\begin{pmatrix} -9&3 \\ 5 &-2 \end{pmatrix}\)

D. \(\begin{pmatrix} 9&-3 \\ 5 &-2 \end{pmatrix}\)

Answer 1

-1= 1|A| adj A 

adj A = |A| x A^-1

= 3 x \(\begin{pmatrix}3&-1 \\-5/ 3 &2/3\end{pmatrix}\)

= \(\begin{pmatrix} 9&-3 \\ -5 &2 \end{pmatrix}\)