Can you help me understand this Algebra question?
(1) Identity for addition (2) Identity for subtraction (3) Identity for multiplication (4) Identity for division (5) Zero property in addition (6) Zero property in subtraction (7) Zero prop. in multiplication (8) Zero property in division 
(9) Property of opposites 10) Property of reciprocals (11) Rounding (12) Inequalities (13) Absolute value (14) Interval notation (15) Not listed 
2. Justify the statement (
−
19)+19=0
(1) Identity for addition (2) Identity for subtraction (3) Identity for multiplication (4) Identity for division (5) Zero property in addition (6) Zero property in subtraction (7) Zero prop. in multiplication (8) Zero property in division 
(9) Property of opposites 10) Property of reciprocals (11) Rounding (12) Inequalities (13) Absolute value (14) Interval notation (15) Not listed 
Justify the statement
−
1
7
(
−
54)
+
1
7
(
−
54)=0
(1) Identity for addition (2) Identity for subtraction (3) Identity for multiplication (4) Identity for division (5) Zero property in addition (6) Zero property in subtraction (7) Zero prop. in multiplication (8) Zero property in division 
(9) Property of opposites 10) Property of reciprocals (11) Rounding (12) Inequalities (13) Absolute value (14) Interval notation (15) Not listed 
Justify the statement
0
−
20
=
20
−
0
(1) Identity for addition (2) Identity for subtraction (3) Identity for multiplication (4) Identity for division (5) Zero property in addition (6) Zero property in subtraction (7) Zero prop. in multiplication (8) Zero property in division 
(9) Property of opposites 10) Property of reciprocals (11) Rounding (12) Inequalities (13) Absolute value (14) Interval notation (15) Not listed, incorrect. 
Justify the statement
−
79
+
0
=
−
79
(1) Identity for addition (2) Identity for subtraction (3) Identity for multiplication (4) Identity for division (5) Zero property in addition (6) Zero property in subtraction (7) Zero prop. in multiplication (8) Zero property in division 
(9) Property of opposites 10) Property of reciprocals (11) Rounding (12) Inequalities (13) Absolute value (14) Interval notation (15) Not listed, incorrect. 
Justify the statement
(
1
17
)
⋅
0
=
0
⋅
(
1
29
)
(1) Identity for addition (2) Identity for subtraction (3) Identity for multiplication (4) Identity for division (5) Zero property in addition (6) Zero property in subtraction (7) Zero prop. in multiplication (8) Zero property in division 
(9) Property of opposites 10) Property of reciprocals (11) Rounding (12) Inequalities (13) Absolute value (14) Interval notation (15) Not listed 
If
(
1
a
)
⋅
0
=
0
⋅
(
1
b
)
then
a
=
b
. True or false? Why?
(1) True because the two sides of an equation must be equal.
(2) True because the two sides of an equation must be 0.
(3) True because the two sides of the equation are 0.
(4) False because the two sides of the equation are 0 regardless of whether
a
=
b
or not, as long as
a
≠
0
and/or
b
≠
0
Justify the statement
1
⋅
(
5.6
)
=
(
5.6
)
⋅
1
(1) Identity for addition (2) Identity for subtraction (3) Identity for multiplication (4) Identity for division (5) Zero property in addition (6) Zero property in subtraction (7) Zero prop. in multiplication (8) Zero property in division 
(9) Property of opposites 10) Property of reciprocals (11) Rounding (12) Inequalities (13) Absolute value (14) Interval notation (15) Not listed 
Justify the statement
1
÷
15
=
15
÷
1
(1) Identity for addition (2) Identity for subtraction (3) Identity for multiplication (4) Identity for division (5) Zero property in addition (6) Zero property in subtraction (7) Zero prop. in multiplication (8) Zero property in division 
(9) Property of opposites 10) Property of reciprocals (11) Rounding (12) Inequalities (13) Absolute value (14) Interval notation (15) Not listed 
Evaluate
0
a
where a=84.
(1) 0
(2) undefined
(3) no solution
(4) infinity
Evaluate
a
0
where a=2.
(1) 0
(2) undefined ( or infinity)
(3) no solution
(4) 1
Justify the statement
(
a
b
)
(
b
a
)
=1 where a=7 and b=71
(1) Identity for addition (2) Identity for subtraction (3) Identity for multiplication (4) Identity for division (5) Zero property in addition (6) Zero property in subtraction (7) Zero prop. in multiplication (8) Zero property in division 
(9) Property of opposites 10) Property of reciprocals (11) Rounding (12) Inequalities (13) Absolute value (14) Interval notation (15) Not listed 
Subtract the opposite of 37 from the reciprocal of

−
1

b
where b=79
Every real number has an opposite.
Every real number has a reciprocal.