Let A = [[a11,a12],[a21,a22]] and B = [[b11,b12],[b21,b22]] be two matrices such that A*B = I. Let C = A^(-1) and D = B^...

Question

Let A = [[a11,a12],[a21,a22]] and B = [[b11,b12],[b21,b22]] be two matrices such that A*B = I. Let C = A^(-1) and D = B^(-1). Express the elements of D in terms of the elements of B.

Accepted Answer

D = B^(-1) = A = [[b22, -b12], [-b21, b11]] / (b11*b22 - b12*b21). We are given that AB = I, which means B = A^(-1) and A = B^(-1). So D = B^(-1) = A. The elements of D are the elements of A. Additionally, for a 2x2 matrix B, the inverse formula gives B^(-1) = (1/det(B)) * [[b22,-b12],[-b21,b11]].