Properties of invertible matrices

Question 1

if A is invertible then

Answer 1

• A is a square matrix
• A^-1 is invertible
• (A^-1)^-1 =A

Question 2

If A is invertible and c is non zero scalar

(cA)^-1

Answer 2

1/c (A^-1)

Question 3

if A and B are both invertible matrices then (AB)^-1

Answer 3

B^-1 A^-1

Question 4

if A is invertible then A^n is invertivle for which values of n

Answer 4

all non negative integers n

Question 5

(A^n)^-1 =

Answer 5

(A^-1)^n

under the conditions that:
- n is a non negative integer
a is invertible

Question 6

generalize the swap products when we do inverse rule to many invertible matrices

Answer 6

(A1 A2 A3…… An)^-1 = An^-1 ……. A3^-1 A2^-1 A1^-1