Use the row reduction method to find the inverse, if it exists.
$A = \left[ \begin{array} { l l }
2 & 5 \
1 & 3
\end{array} \right]$
A) $\left[ \begin{array} { l l }
- 2 & - 5 \
- 1 & - 3
\end{array} \right]$
B) $\left[ \begin{array} { c c }
- 3 & 5 \
1 & - 2
\end{array} \right]$
C) $\left[ \begin{array} { l l }
\frac { 1 } { 2 } & 0 \
0 & \frac { 1 } { 3 }
\end{array} \right]$
D) $\left[ \begin{array} { c c }
3 & - 5 \
- 1 & 2
\end{array} \right]$
E) no inverse exists

Question

Use the row reduction method to find the inverse, if it exists.   
$A = \left[ \begin{array} { l l } 
2 & 5 \
1 & 3
\end{array} \right]$  
A) $\left[ \begin{array} { l l } 
- 2 & - 5 \
- 1 & - 3
\end{array} \right]$
B)   $\left[ \begin{array} { c c } 
- 3 & 5 \
1 & - 2
\end{array} \right]$
C) $\left[ \begin{array} { l l } 
\frac { 1 } { 2 } & 0 \
0 & \frac { 1 } { 3 }
\end{array} \right]$
D) $\left[ \begin{array} { c c } 
3 & - 5 \
- 1 & 2
\end{array} \right]$
E) no inverse exists

Quizplus · Accepted Answer

The determinant of matrix A is $2*3 - 5*1 = 6 - 5 = 1$, which is non-zero, indicating that an inverse exists. The formula for the inverse of a 2x2 matrix $A = \left[ \begin{array} { c c } a & b \ c & d \end{array} \right]$ is $A^{-1} = \frac{1}{ad-bc} \left[ \begin{array} { c c } d & -b \ -c & a \end{array} \right]$. Applying this formula to matrix A gives $A^{-1} = \frac{1}{1} \left[ \begin{array} { c c } 3 & -5 \ -1 & 2 \end{array} \right]$, which matches option D.

Use the Row Reduction Method to Find the Inverse, If A=[2513]A = \left[ \begin{array} { l l } 2 & 5 \\1 & 3\end{array} \right]A=[21​53​]

Use the Row Reduction Method to Find the Inverse, If $A = \left[ \begin{array} { l l } 2 & 5 \\1 & 3\end{array} \right]$