Finding Matrix B from given info

[xipe]

Homework Statement

Use the given info to find matrix B

Homework Equations

(I + 3B)^-1 = [5 2; 4 2]

to make more clear:

inv(I + 3B) = this 2x2 matrix: top row = 5 2, bottom row = 4 2

The Attempt at a Solution

I tried multiplying both sides of the eqn by I + 3B to get I = [5 2; 4 2](I + 3B)
Then tried to multiply the two quantities (using B = [a b; c d])
Tried to set that product equal to the identity matrix and solve for the unspecified constants, a b c d.
After that I plugged the values into the the product found in the previous step
I then should have acquired the correct matrix B, but alas, it wasn't even close.
If I am overlooking some elementary matrix 'algebra', or any hints at all would be greatly appreciated.
Thank you!

 

[Fightfish]

Why not just calculate the matrix inverse of the 2x2 matrix on the RHS?