# Suppose that: E_4 [[1,3,4],[2,2,3],[-5,4,4]] = [[1,3,4],[8,8,12],[-5,4,4]] Find E_4 and (E_4)^-1

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`E_4` is an elementary matrix. That is, one that can be reached from the identity matrix of the same dimension by an elementary operation.

In this case the operation is multiplying row 2 by 4.

Therefore `E_4 = ((1,0,0),(0,4,0),(0,0,1))`

`E_4^(-1)` is also an elementary matrix and is simply the inverse operation, ie dividing row 2 by 4. So that

`E_4^(-1) = ((1,0,0),(0,1/4,0),(0,0,1))`

**answer**