Read the following algebra question. Also, provide an explanation with the answer along with working

Definition Read the following definition, and answer the question that follows. We say that an nxn matrix A is never sad if for any rx1 matrix x + 0, the matrix product x'Ax is a non-negative number. (Note that x' Ax is indeed aturays a number since the dimensions of the three matrices being multiplied are 1 xnnx n and nx 1! Also note that non negative manns gater than or equal to 0) Show that if a 3 x 3 matrix A is never sad then the entries along its diagonal, i.e. 011, 222, 233, must be non-negative