# SOLUTION: Find the inverse of the matrix if it exists.? A= [1,-2] [1,2] A^-1=

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Question 627192: Find the inverse of the matrix if it exists.?
A=
[1,-2]
[1,2]
A^-1=

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Solved by pluggable solver: Finding the Inverse of a 2x2 Matrix

To find the inverse of the matrix , we can follow these steps:

### Step 1) Find the determinant

The determinant of is . So this means that

### Step 2) Swap the values

Now switch the highlighted values to get

### Step 3) Change the sign

Now change the sign of the highlighted values to get

### Step 4) Multiply by the inverse of the determinant

Multiply by to get

Plug in to get

### Step 5) Multiply by every element in the matrix (simplify and reduce if possible)

Multiply by EVERY element to get

Multiply to get

Reduce each element:

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So the inverse of is

This means that if then