The inverse of matrix N = \(\begin{vmatrix} 2 & 3 \\
1 & 4\end{vmatrix}\) is

A.

\(\frac{1}{5}\) \(\begin{vmatrix} 2 & 1 \\ 3 & 4\end{vmatrix}\)

B.

\(\frac{1}{5}\) \(\begin{vmatrix} 4 & -3 \\ -1 & 2\end{vmatrix}\)

C.

\(\frac{1}{5}\) \(\begin{vmatrix} 2 & -1 \\ -3 & 4\end{vmatrix}\)

D.

\(\frac{1}{5}\) \(\begin{vmatrix} 4 & 3 \\ 1 & 2\end{vmatrix}\)

Correct answer is B

N = [2 3]

N-1 = \(\frac{adj N}{|N|}\)

adj N = \(\begin{vmatrix} 4 & -3 \\ -1 & 2 \end{vmatrix}\)

|N| = (2 x4) - (1 x 3)

= 8 - 3

=5

N-1 = \(\frac {1}{5}\) \(\begin{vmatrix} 4 & -3 \\ -1 & 2 \end{vmatrix}\)