41. Show that (AB)T = BTAT if A and B are arbitrary 2 × 2 matrices. A = (a a11 a12 B = , a21 a22 b11 b12 b21b22

Show that P(x)=2x39x2+7x+6 has at least one real zero between 1and0.

Prove that the altitude drawn to the hypotenuse of a right triangle separates the right triangle into two right triangles that are similar to each other and to the original right triangle.

Does the relation is a brother of have a reflexive property consider one male? A symmetric property consider two males? A transitive property consider three males?