The correct option is A Both statement 1 and statement 2 are true and statement 2 is the correct explaination of statement 1.
Statement 1:|A|=∣∣
∣∣5678910111213∣∣
∣∣
Perfoming row operations as follows: R3→R3−R2
|A|=∣∣
∣∣5678910333∣∣
∣∣
Now R2→R2−R1
|A|=∣∣
∣∣567333333∣∣
∣∣=0
So A−1 doesn't exist.
We know that (AB)−1=B−1A−1As A−1 doesn't exists, (AB)−1 doesn't exists.Statement 2 is also true
Hence both statements are true and statement 2 is correct explanation of statement 1.