Question

What is the inverse of

Answer 1

`A^(-1) = (1)/(66) \left[\begin{array}{cc}-2&-5\\6&-18\end{array}\right]`

Explanation:

Given

`A = \left[\begin{array}{cc}-18&5\\-6&-2\end{array}\right]`

Required

Determine the inverse

A matric is of the form:

`A = \left[\begin{array}{cc}a&b\\c&d\end{array}\right]`

First, we need to calculate the determinant (D)

`D = a * d - b * c`

By comparison, we have:

`D = (-18 * -2) - (5 * -6)`

`D = (36) - (-30)`

`D = 36 +30`

`D = 66`

The inverse is then represented as:

`A^(-1) = (1)/(D) \left[\begin{array}{cc}d&-b\\-c&a\end{array}\right]`

This gives:

`A^(-1) = (1)/(66) \left[\begin{array}{cc}-2&-5\\6&-18\end{array}\right]`