# Are the following statements true or false? Here A is an n by n square matrix. 1. If A is not invertible then the system A(vector x) = vector b has infinitely many solutions. 2.The zero matrix is...

Are the following statements true or false? Here A is an n by n square matrix.

**1.** If A is not invertible then the system A(vector x) = vector b has infinitely many solutions.

**2.**The zero matrix is invertible.

**3.**The product of two elementary matrices is an elementary matrix.

**4.** If A is invertible then so is A^T.

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### 1 Answer

1. Not true

let

2x+4y=9

4x+10y=11

`[[2,5],[4,10]][[x],[y]]=[[9],[11]]`

`AX=b`

A is not invertible,

Also it has no solution.

2. Not true.

4. True.

3. True