Lookup value and return max absolute in a range

Hi, I have 2 columns of numbers A and B, how do I return the max absolute value in column B when I lookup a value from column A?
For example, I want to lookup 2 to return the max absolute value is which 100 and 1 to return -10 and 5 to return 40 etc.

Thanks for your help!

A B

1 -10
1 -5
1 0
1 4
1 6
2 10
2 100
2 -50
2 -5
2 10
5 -2
5 40
5 -9
5 -10
5 -3

Hello! Please see text below:

A B Max Number Result
1 -10 6
1 -5 6
1 0 6
1 4 6
1 6 6
2 10 100
2 100 100
2 -50 100
2 -5 100
2 10 100
5 -2 40
5 40 40
5 -9 40
5 -10 40
5 -3 40

The first value of "1" is in cell A2, first value =10 is in cell B2, and the first formula is in cell C2 (drag it down). The formula in cell C2 is: {=MAX(($A$2:$A$16=$A2)*List)} - it's an array formula, so you need to press CTRL+SHIFT+ENTER. The reason the max result for value "1" is 6 is because 6 is a positive number and -10 is a negative number. 6 is larger than -10. List is cells B2:B16.

I hope this is what you were looking for.