Question:
If $\begin{pmatrix} e & f \\ g & h \end{pmatrix}$ is the inverse of the matrix $\begin{pmatrix} a & b \\ c & d \end{pmatrix}$ where $ad - bc = 1$, then $g$ equals
If $\begin{pmatrix} e & f \\ g & h \end{pmatrix}$ is the inverse of the matrix $\begin{pmatrix} a & b \\ c & d \end{pmatrix}$ where $ad - bc = 1$, then $g$ equals
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Always memorize inverse of $2\times2$ matrix—it saves time in exams.
Updated On: Apr 30, 2026
- $c$
- $-c$
- $b$
- $-b$
- $d$
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The Correct Option is B
Solution and Explanation
Concept:
Inverse of a $2 \times 2$ matrix:
\[
\begin{pmatrix} a & b \\ c & d \end{pmatrix}^{-1}
=
\frac{1}{ad-bc}
\begin{pmatrix} d & -b \\ -c & a \end{pmatrix}
\]
Step 1: Use given determinant. \[ ad - bc = 1 \] So inverse becomes: \[ \begin{pmatrix} d & -b \\ -c & a \end{pmatrix} \]
Step 2: Compare with given matrix. \[ \begin{pmatrix} e & f \\ g & h \end{pmatrix} = \begin{pmatrix} d & -b \\ -c & a \end{pmatrix} \]
Step 3: Identify $g$. \[ g = -c \]
Final Answer: \[ \boxed{-c} \]
Step 1: Use given determinant. \[ ad - bc = 1 \] So inverse becomes: \[ \begin{pmatrix} d & -b \\ -c & a \end{pmatrix} \]
Step 2: Compare with given matrix. \[ \begin{pmatrix} e & f \\ g & h \end{pmatrix} = \begin{pmatrix} d & -b \\ -c & a \end{pmatrix} \]
Step 3: Identify $g$. \[ g = -c \]
Final Answer: \[ \boxed{-c} \]
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