If A is nonsingular and B is nonsingular show that A - B is nonsingular
is this true or false and why ...
my answer
False cuase
A is nonsingular then det A =/ 0
B is nonsingular then det B =/ 0
det ( A - B ) =/ 0
det A - det B =/ 0
det A =/ det B
that mean that A - B nonsingular if and only if det A =/ det B
is my answer right
thankful
@ Sadeem Zone , indeed, you still have some way to go. But don't worry, you are almost right.
If the entries of $A,B$ follow (independently) the normal law $N(0,1)$, then $prob(A,B,A+B \text{ are invertible })=1$.
More generally, if $P,Q,R,S$ are randomly chosen (as above), then $Pdiag(I_p,0_{n-p})Q+Rdiag(0_p,I_{n-p})S$ is invertible with probability $1$.