Suppose that A B and C are n x n matrices with B invertable

Suppose that A, B, and C are n x n matrices with B invertable and I-BAB^-1=C

a. Solve the equation for A, show steps.

b. Contruct 2x2 matrces A, B, and C that satisfy a, where B is not a multiple of I₂.

c. Is A always invertable? let C=

, explain?

Solution

A is always invertable