Question

Consider the matrix shown below:

Answer 1

Answer:

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

Step-by-step explanation:

Given the matrix: $\left[\begin{array}{ccc}2&5\\3&8\\\end{array}\right]$,  it's inverse is calculated using the formula:

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

#Therefore, we calculate as;

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

Hence, the inverse of the matrix is $\left[\begin{array}{ccc}8&-5\\-3&2\\\end{array}\right]$