Convexity of the Frobenius norm of the product of matrix and its transpose

Question

$B$ and $X$ are fixed matrix. The transpose of a matrix is denoted by ^T. $||.||_F$ denotes Frobenius norm.

Is $f(A)=||B - X^TA^TAX||_F^2$ convex function or non-convex function?

Answer 1

Let's look at the simplest possible case: $n=B=X=1$.

Is $f(A) = (1-A^2)^2$ convex?