true or false

Question

 If A is a square matrix with inverse A-¹ and c is a nonzero real number, then  ( cA)^-1=1/c A^-1

 

True or False

 

If you think the statement is true, then show that it is true. On the other hand, if you think the statement is false, then give an example that disproves the statement.

Answer 1

Let A =[1 2

3 4 ], cA = [c 2c ]

[3c. 4c]

(cA)^(-1)=1/(4c^2-6c^2)=1/(-2c^2)[4c. -2c]

[-3c. C]=

(-1/2c)[ 4 -2 -3 1]

Other side

1/c[ 1 2 3 4]^(-1)=1/c [4 -2 -3 1]

This proves it for the 2x2 matrix [1 2 3 4]