Two $n$ by $n$ matrices $M,N$ with real entries are called strongly independent if the matrix $aI+bM+cN$ is invertible for any real numbers $a,b,c$ which are not all $0$.

a) Show that if $MN=NM$ then $M,N$ are not strongly independent.

b) For any $n$ which is a multiple of 4 construct two strongly independent matrices of size $n$.

(Here $I$ denotes the identity matrix.)