Question

Consider the matrix shown below:

Answer 1

A)

`A^(-1)={\left[\begin{array}{ccc}8&-5\\-3&2\\\end{array}\right]}`

Explanation:

Given the following matrix
`\left[\begin{array}{ccc}2&5\\3&8\\\end{array}\right]`, its inverse is calculated using the formula:

`\left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right] ^(-1)=\frac{1}{det\left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right]}\left[\begin{array}{ccc}d&-b\\-c&a\\\end{array}\right]`

#We can therefore calculate the inverse of our matrix as follows:

`\frac{1}{det\left[\begin{array}{ccc}2&5\\3&8\\\end{array}\right]}\left[\begin{array}{ccc}8&-5\\-3&2\\\end{array}\right]\\\\\\\\{det\left[\begin{array}{ccc}2&5\\3&8\\\end{array}\right]}=1\\\\\\\\\therefore =(1)/(1){\left[\begin{array}{ccc}8&-5\\-3&2\\\end{array}\right]}\\\\\\\\={\left[\begin{array}{ccc}8&-5\\-3&2\\\end{array}\right]}`

Hence, the inverse of the matrix is

`A^(-1)={\left[\begin{array}{ccc}8&-5\\-3&2\\\end{array}\right]}`