If A=1-11-1&B=1a4b&(A+B)2=A2+B2. Then a&b are respectively
1,-1
2,-3
-1,1
3,-2
Explanation for the correct option.
Step1. Given that,
A=1-11-1&B=1a4b&(A+b)2=A2+B2
Step2. Finding the value of a & b.
Now,
A=1-12-1;B=1a4b⇒(A+B)=2a-16b-12a-16b-1⇒(A+B)2=-2+6aa-1-b+ab6+6b5a-5-2b+b2A2=1-1211-121=-100-1B2=1a4b1a4b=1+4aa+9b4+4b4a+b2As(A+B)2=A2+B2⇒-2+6aa-1-b+ab6+6b5a-5-2b+b2=-100-1+1+4aa+9b4+4b4a+b2⇒-2+6aa-1-b+ab6+6b5a-5-2b+b2=4aa+9b4+4b4a+b2-1∴-2+6a=4a⇒a=1⇒6+6b=4+4b⇒b=-1
Therefore the value of (a, b) is (1,-1)
Hence, correct option is (A)