In questions determine whether the statement is true or false.
-$$\text { If } \mathbf { A } = \left( \begin{array} { l l }
3 & 5 \
1 & 2
\end{array} \right) , \text { then } \mathbf { A } ^ { - 1 } = \left( \begin{array} { c c }
2 & 5 \
1 & - 3
\end{array} \right)$$

Question

In questions determine whether the statement is true or false.
-$$\text { If } \mathbf { A } = \left( \begin{array} { l l } 
3 & 5 \
1 & 2
\end{array} \right) , \text { then } \mathbf { A } ^ { - 1 } = \left( \begin{array} { c c } 
2 & 5 \
1 & - 3
\end{array} \right)$$

Quizplus · Accepted Answer

The inverse of a 2x2 matrix $\mathbf{A} = \begin{pmatrix} a & b \ c & d \end{pmatrix}$ is $\mathbf{A}^{-1} = \frac{1}{ad-bc} \begin{pmatrix} d & -b \ -c & a \end{pmatrix}$. For $\mathbf{A} = \begin{pmatrix} 3 & 5 \ 1 & 2 \end{pmatrix}$, the determinant is $3(2) - 5(1) = 1$, so $\mathbf{A}^{-1} = \begin{pmatrix} 2 & -5 \ -1 & 3 \end{pmatrix}$.

In Questions Determine Whether the Statement Is True or False