Question

what is the inverse of

Answer 1

Answer:

$A^{-1} = \frac{1}{66} \left[\begin{array}{cc}-2&-5\\6&-18\end{array}\right]$

Step-by-step 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:

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

This gives:

$A^{-1} = \frac{1}{66} \left[\begin{array}{cc}-2&-5\\6&-18\end{array}\right]$