Suppose A is a 2 x 2 matrix which is leftinvertible That is

Suppose A is a 2 x 2 matrix which is left-invertible. That is, there is a 2 x 2 matrix c such that CA = I. Which of the following must be true?

a) A cannot be a diagonal matrix.

c) C cannot be a diagonal matrix.

d) C is also left-invertible.

e) AC = -CA

We have the rule here that if A and B are two matrices of same order such that

AB=I=BA

then B is called invertical matrix of A. That means A has a left inverse also such that BA= I also.

Thus C is also a left invertible.

So only option d) is correct answer here that is true.