# Thread: help with proving nonsingular

1. ## help with proving nonsingular

(1) if A and B are nonsingular matrics, which, if any of the following must be nonsingular?

(a) A+B (b) (AB)^2 (c) kA (k subeset R)

justify your answer either be obtaining the inverse or by a counter example to show it need not exist.

(2) if A,B and C are square matrices, such that AB = In and CA = In, prove that A is nonsigular and B = C = A^-1.
(Hint: try multiplying AB and CA by C and B respectively)

For (1), I know (b) and (c) is true, how about (a)? And I dunno how to start (2)

2. Originally Posted by 450081592
(1) if A and B are nonsingular matrics, which, if any of the following must be nonsingular?

(a) A+B (b) (AB)^2 (c) kA (k subeset R)

justify your answer either be obtaining the inverse or by a counter example to show it need not exist.

(2) if A,B and C are square matrices, such that AB = In and CA = In, prove that A is nonsigular and B = C = A^-1.
(Hint: try multiplying AB and CA by C and B respectively)

For (1), I know (b) and (c) is true,

(c) is true iff $0\neq k\in \mathbb{R}$

The hint is a very good place where to start: $AB=I=CA\Longrightarrow C=CI=C(AB)=(CA)B=...$