If A = ((2,5),(1,3)) then adj A = ? ​

Question

If A = \(\begin{pmatrix} 2&5 \\ 1 &3 \end{pmatrix}\) then adj A = ?

A. \(\begin{pmatrix} 3&-5 \\ -1 &2 \end{pmatrix}\)

B.\(\begin{pmatrix} 3&-1 \\ -5 &2 \end{pmatrix}\)

C.\(\begin{pmatrix} -1&2 \\ 3 &-5 \end{pmatrix}\)

D. None of these

Answer 1

To find adj A we will first find the cofactor matrix 

C₁₁ = 3 C₁₂ = -1 

C₂₁= -5 C₂₂ = 2

Cofactor matrix A = \(\begin{pmatrix} 3&-1 \\ -5 &2 \end{pmatrix}\)

Adj A = \(\begin{pmatrix} 3&-1 \\ -5 &2 \end{pmatrix}\)

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