If `A=[(5a,-b),(3, 2)]` and `A adj A=A A^T` , then `5a+b` is equal to: (1) `-1` (2) 5 (3) 4 (4) 13

Options

A. 5
B. 4
C. 13
D. `-1`

Answer

A

Explanation

A adj `A=A A^(T)`
`implies |A|I=A A^(T)`
`implies (10a+3b) [(1,0),(0,1)]=[(5a,-b),(3,2)][(5a,3),(-b,2)]`
`implies 25a^(2)+b^(2)=10a+3b, 15a-2b=0, 10a+3b=13`
`implies 10a+(3.15a)/2=13`
`implies 65a=2xx13`
`implies a=2/5`
`implies 5a=2`
`implies 2b=6`
`implies b=3`
`:. 5a+b=5`