Question

The inverse of matrix $A = \begin{bmatrix} a & b \\ c & d \end{bmatrix}$is

• A. $\begin{bmatrix} d & - b \
  • c & a \end{bmatrix}$
• B. $\frac{1}{ad - bc}\begin{bmatrix} d & - b \
  • c & a \end{bmatrix}$ `
• C. $\frac{1}{|A|}\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$
• D. $\begin{bmatrix} b & - a \\ d & - c \end{bmatrix}$

Answer 1

Answer: (B)

$\frac{1}{ad - bc}\begin{bmatrix} d & - b \

• c & a \end{bmatrix}$ `

Answer 2

Here$|A| = \left| \begin{matrix} a & b \\ c & d \end{matrix} \right| = ad - bc$, $adj(A) = \begin{bmatrix} d & - b \

• c & a \end{bmatrix}$.

Hence $A^{- 1} = \frac{1}{ad - bc}\begin{bmatrix} d & - b \

• c & a \end{bmatrix}$