: Suppose A is invertible and orthogonally diagonalizable. Explain why A -1 is also orthogonally diagonalizable. where P is orthogonal and D is diagonal. Because A is invertible, to Matrix A is orthogonally diagonalizable, so A= diagonalizable. DPD 1 PDP-1 1 hy A is also orthogonally diagonalizable. Since D is diagonal, D 11 is orthogonal and Dis diagonal. Because Ais invertible, this equation yields A PDP p-10-12 PDP. PDP-1 PDP PDP-1 -1 quation yields A -1 Since D is diagonal, D is - 1 Therefore, A is also orthogonally orthogonal diagonal