Let A , B , C be 3 × 3 matrices such that A is symmetric and B and C are skew-symmetric. Consider the statements S 1 A 13 B 26 - B 26 A 13 is symmetric S 2 A 26 C 13 - C 13 A 26 is symmetric Then,

Step-by-step solution

Given, Matrix A is symmetric, B is skew symmetric and C is skew symmetric, So, A T = A ,   B T = - B ,   C T = - C Now let M = A 13 B 26 - B 26 A 13 Then, M T = A 13   B 26 - B 26   A 13 T = A 13 B 26 T - B 26   A 13 T = B T 26   A T 13 - A T 13   B T 26 = B 26   A 13 - A 13   B 26 = - M Hence, M is skew symmetric Now let, N = A 26 C 13 - C 13   A 26 Then, N T = A 26 C 13 T - C 13 A 26 T = - C 13 A 26 + A 26 C 13 = N Hence, N is symmetric. So, only S 2 is true.