Question

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Answer 1

Answer:

$\begin{bmatrix}-1 & 2 \\ \frac{3}{2} & -\frac{5}{2} \end{bmatrix}$

Step-by-step explanation:

Inverse of a matrix is given by,

$\begin{bmatrix}a & b\\ c & d\end{bmatrix}=\frac{1}{ad-bc}\begin{bmatrix}d & -b\\ -c & a\end{bmatrix}$

By using this property,

$\begin{bmatrix}5 & 4\\ 3 & 2\end{bmatrix}^{-1}=\frac{1}{(5\times 2-4\times 3)}\begin{bmatrix}2 & -4\\ -3 & 5\end{bmatrix}$

              $=-\frac{1}{2}\begin{bmatrix}2 & -4\\ -3 & 5\end{bmatrix}$

              $=\begin{bmatrix}-1 & 2 \\ \frac{3}{2} & -\frac{5}{2} \end{bmatrix}$

Therefore, inverse of the given matrix will be $\begin{bmatrix}-1 & 2 \\ \frac{3}{2} & -\frac{5}{2} \end{bmatrix}$