# True or false? 1. If det(A)=0 then A=0. 4. If det(A) = 3 then det(2A) = 6. 5. If A is a 2x2 matrix with zero determinant, then one column of A must be a multiple of the other one.

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### 1 Answer

Det(A)=0 does not mean A=0

`A=[[1,0],[1,0]]`

`|A|=0 `

`` But A`!=0`

`A=[[1,0],[0,1]]`

`|A|=1`

`2A=[[2,0],[0,2]]`

`|2A|=4`

`!=2` det(A)

`A=[[2,1],[2,1]]`

`|A|=0`

One column is multiple of the other.

We need more observation.