Let A and B be square matrices. Show that if AB = I then A and B are both invertible, with B =A1 and A=B¯¹ It is given that AB = I. The Invertible Matrix Theorem states that if there is an nxn matrix B such that AB = I, then it is true that It is given that AB = I. The Invertible Matrix Theorem states that if there is an nxn matrix A such that AB = I, then it is true that It is given that AB = I. Left-multiply each side of the equation by A¯ 1 A¹AB = A¹I = A-1 Left-multiply by A1 Simplify. It is given that AB = I. Right-multiply each side of the equation by B¹ ABB 1 = IB = B1 In conclusion, it can be stated that A and B Right-multiply by B1 Simplify. with B = and A=