Question

Consider the matrix shown below:

Answer 1

Answer:

A)

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

Step-by-step 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:

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

Hence, the inverse of the matrix is

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