SOLUTION: Find the inverse of the following matrices MAT (A) = ((9 -8 3 16))

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Question 1164041: Find the inverse of the following matrices
MAT (A) = ((9 -8
3 16))
Answer by Edwin McCravy(20062) About Me  (Show Source):
You can put this solution on YOUR website!
A+=+%28matrix%282%2C2%2C9%2C-8%2C3%2C16%29%29

First swap the upper left and lower right diagonal elements

%28matrix%282%2C2%2C16%2C-8%2C3%2C9%29%29

Change the signs of upper right and lower left diagonal elements

%28matrix%282%2C2%2C16%2C8%2C-3%2C9%29%29

Calculate the determinant of the original matrix, [or the determinant of
either of these, as they all have the same determinant:

(9)(16)-(-8)(3) = 144-(-24) = 144+24 = 168

Divide each term by the value of the determinant

%28matrix%282%2C2%2C16%2F168%2C8%2F168%2C-3%2F168%2C9%2F168%29%29

Reduce any fractions that will reduce (they all will)

A%5E%28-1%29=%28matrix%282%2C2%2C2%2F21%2C1%2F21%2C-1%2F56%2C3%2F56%29%29

This method works ONLY for 2x2 matrices.

Edwin