Method 1 is as follows.

[1] Interchange leading diagonal elements:

`-7 → 2`; `2 → -7`

`((-7,-3),(4,2))`

[2] Change signs of the other 2 elements:

`-3 → 3`; `4 → -4`

`((-7,3),(-4,2))`

[3] Find the determinant `|A|`

`|(2,-3),(4,-7)|=-14+12=-2`


[4] Multiply result of [2] by `1/|A|`

`A^-1 = 1/|A|((-7,3),(-4,2))`

`=1/(-2)((-7,3),(-4,2))`

`=((3.5,-1.5),(2,-1))`

So we have found the inverse, as required.

Is it correct?

We check by multiplying our inverse by the original matrix. If we get the identity matrix (I) for our answer, then we must have the correct answer.

`A^-1A=((3.5,-1.5),(2,-1))((2,-3),(4,-7))`

`=((7-6,-10.5+10.5),(4-4,-6+7))`

`=((1,0),(0,1))`

`=I`

We can go to bed happy, knowing that our answer is correct.

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