If A = ((a,b),(c,d)) then adj A = ? ​

Question

If A = \(​​​​\begin{pmatrix} a & b \\ c & d \\ \end{pmatrix}\)then adj A = ?

((a,b),(c,d))

A. \(​​​​\begin{pmatrix} d& -c \\ -b & a \\ \end{pmatrix}\)

B. \(​​​​\begin{pmatrix} -d & b \\ c & -a \\ \end{pmatrix}\)

C. \(​​​​\begin{pmatrix} d &-b \\ -c & a \\ \end{pmatrix}\)

D.\(​​​​\begin{pmatrix} -d &-b \\ c & a \\ \end{pmatrix}\)

Answer 1

To find adj A we will first find the cofactor matrix 

C₁₁ = d C₁₂ = -c 

C₂₁= -b C₂₂ = a 

Cofactor matrix A = \(​​​​\begin{pmatrix} d& -c \\ -b & a \\ \end{pmatrix}\)

Adj A = \(​​​​\begin{pmatrix} d& -c \\ -b & a \\ \end{pmatrix}\)

= \(​​​​\begin{pmatrix} d& -c \\ -b & a \\ \end{pmatrix}\)