# Given `det [[a,b,c],[d,e,f],[g,h,i]] = -1` , find the following determinants c) `det [[-8a+6d, -8b+6e, -8c+6f],[g,h,i],[2d,2e,2f]]`

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### 1 Answer

`det [[-8a+6d, -8b+6e, -8c+6f],[g,h,i],[2d,2e,2f]]=`

Adding one row multiplied by a scalar to another row does not change the value of determinant.

`det [[-8a, -8b, -8c],[g,h,i],[2d,2e,2f]]=`

When rows change places determinant changes sign (plus to minus and vice versa).

`-det [[-8a, -8b, -8c],[2d,2e,2f],[g,h,i]]=`

When we multiply a row with a scalar the determinant is multiplied by the same scalar.` `

`(-8)2(-1)det [[a, b, c],[d,e,f],[g,h,i]]=16cdot(-1)=-16`