Question

Adjoint of matrix $A=\left[\begin{array}{cc}4& 5\\ 6& 7\end{array}\right]$ is

[2 marks]

• A. $\left[\begin{array}{cc}4& 6\\ 5& 7\end{array}\right]$
• B. $\left[\begin{array}{cc}-4& 5\\ 6& -7\end{array}\right]$
• C. $\left[\begin{array}{cc}7& -5\\ -6& 4\end{array}\right]$
• D. $\left[\begin{array}{cc}7& 4\\ 5& 6\end{array}\right]$

Answer 1

The correct option is C $\left[\begin{array}{cc}7& -5\\ -6& 4\end{array}\right]$

$A=\left[\begin{array}{cc}4& 5\\ 6& 7\end{array}\right]$
We have $A_{11}=7,A_{12}=-6,A_{21}=-5,A_{22}=4$
Hence, $adj\left(A\right)={\left[\begin{array}{cc}7& -6\\ -5& 4\end{array}\right]}^T=\left[\begin{array}{cc}7& -5\\ -6& 4\end{array}\right]$