Question

3. Which of the following is NOT always true about matrices A, B, and C? A. If AB = 0, then either A=0 or B=0 B. If A is invertible and AB = AC ,then B = C C. If A is singular, then its transpose is also singular D. If B is the inverse A, then the transpose of B is the Inverse of the transpose of A 20​

Answer 1

The statement that is NOT always true about matrices A, B, and C is:

C. If A is singular, then its transpose is also singular.

Explanation:

A matrix A is singular if and only if its determinant is zero. However, the transpose of a matrix does not necessarily have the same determinant as the original matrix. So, it is possible for a matrix A to be singular while its transpose is non-singular. Therefore, statement C is not always true.