Mutliply both sides by A, giving:

Which gives:

Multiply both sides by the inverse of B

giving:

And note that the inverse of matrix B is given by

PS: for a 2x2 matrix:

[a b]

[c d]

then the Adjacent (Adj) of that matrix is given by:

[d -b]

[-c a]

And you should know that the determinant of said matrix is:

ad-cb