Explain why the following statements/arguments are wrong. (a) If A and B are two square matrices such that AB = O, then A = 0 or B = 0. 1 1 3 (b) 1 3 0 0 1 -1 = + 10 + 3

PODASIP the following statements about products and inverses of triangular and unit triangular matrices. a. The inverse of a triangular matrix is triangular. b. The product of two triangular matrices is triangular. c. The inverse of a unit upper (lower) triangular matrix is upper (lower) triangular. d. The product of two-unit triangular matrices is unit triangular.

Let 4 A = 0 -11 -6 1 Write A as a product of elementary matrices.

Show that for any square matrices A and B, Tr (AB) = Tr (BA).