For any two matrices

$$

A and

$$

B $($assuming all products exist$),$

$$

$$

$$

$$

$$

$$

$$

$$

$$

$=(1)$

$$

$$

$$

$$

$$

$$

$$

$$

$$

$$

$$

$$

$$

$=(2)$

$$

$$

$0$

$$AB$$BA$$

$=$

$(1)$

$$AB$$BA$$

$=$

$(2)$

$0$

This statement is: $($choose the most correct answer$)$

The following multiple$-$choice options contain math elements, so you may need to read them in your screen reader's $$reading$$ or $$browse$$ mode instead of $$forms$$ or $$focus$$ mode.

Choice $1$ of $4$:True

Choice $2$ of $4$:False because the jump through

$=(1)$

$=$

$(1)$

is not valid.

Choice $3$ of $4$:False because the jump through

$=(2)$

$=$

$(2)$

is not valid

Choice $4$ of $4$:False because the jump through

$=(1)$

$=$

$(1)$

and

$=(2)$

$=$

$(2)$

are both not valid