Question

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Answer 1

`\begin{bmatrix}-1 & 2 \\ (3)/(2) & -(5)/(2) \end{bmatrix}`

Explanation:

Inverse of a matrix is given by,

`\begin{bmatrix}a & b\\ c & d\end{bmatrix}=(1)/(ad-bc)\begin{bmatrix}d & -b\\ -c & a\end{bmatrix}`

By using this property,

`\begin{bmatrix}5 & 4\\ 3 & 2\end{bmatrix}^(-1)=(1)/((5* 2-4* 3))\begin{bmatrix}2 & -4\\ -3 & 5\end{bmatrix}`

`=-(1)/(2)\begin{bmatrix}2 & -4\\ -3 & 5\end{bmatrix}`

`=\begin{bmatrix}-1 & 2 \\ (3)/(2) & -(5)/(2) \end{bmatrix}`

Therefore, inverse of the given matrix will be
`\begin{bmatrix}-1 & 2 \\ (3)/(2) & -(5)/(2) \end{bmatrix}`