If A is 3x3 matrix and detA = 2

i understand how to do stuff with determinants if i had a fuction before but this don't really understand and i know i cant add the 2 determinants,

thanks.

p.s. I tried to write it in latex but the ^-1 wouldn't work it would only put the negative sign in superscript

alright so i know that A^-1 = adj(A)det(A)^-1

so by this

det(A^-1 + 4(A^-1)(detA)) since detA = 2
det(A^-1 + 8A^-1)
det(9A^-1) since I = A(A^-1) since A has an inverse we know its invertible and this is true
9Det(I)
------- = 9/2
Det(A)

can someone verify that my algebra is correct cus I'm not too sure

2. Originally Posted by treetheta
If A is 3x3 matrix and detA = 2

i understand how to do stuff with determinants if i had a fuction before but this don't really understand and i know i cant add the 2 determinants,

thanks.

p.s. I tried to write it in latex but the ^-1 wouldn't work it would only put the negative sign in superscript

alright so i know that A^-1 = adj(A)det(A)^-1

so by this

det(A^-1 + 4(A^-1)(detA)) since detA = 2
det(A^-1 + 8A^-1)
det(9A^-1) since I = A(A^-1) since A has an inverse we know its invertible and this is true
9Det(I)
------- = 9/2
Det(A)

can someone verify that my algebra is correct cus I'm not too sure
You are right if you meant "det(A^-1 + 4Adj A)"