Thread: Proof for matrix

This proof was confusing me so if anyone could show me how it is done, then i would appreciate it!

If A is a nonsingular matrix and c is in the set of real numbers w/ c not equal to 0, prove that the inverse of cA (meaning (cA)^-1) is equal to the inverse of A * (1/c).

Originally Posted by buckaroobill

This proof was confusing me so if anyone could show me how it is done, then i would appreciate it!

If A is a nonsingular matrix and c is in the set of real numbers w/ c not equal to 0, prove that the inverse of cA (meaning (cA)^-1) is equal to the inverse of A * (1/c).

I think you mean that,
(cA)^-1=(1/c)*A^-1

This is easy.

Just show that,
[cA][(1/c)A^-1]=Identity.

This is true because c(1/c)=1
And A*A^-1=Identity.

Thus this statement is true.

Ah! Got it! Thanks!