I really need some clarification about cofactors and adj of a 2x2 matrix

say the matrix is

a b

c d

what would the cofactors be?

what would the adj be?

this is what i think but for some reason i think its different.

cofactor

d -c

-b a

adj

d -b

-c a

thanks for any clarification about this. i would really appreciate it cause my professor decided to skip this part of the chapter yet its on my online hw

Thank you