Question

Following are the statements for a square matrix A:
A. If A is invertible then $det(A) \neq 0$
B. If $det(A) = 0$, A has no inverse
C. All eigen values of A are always positive
D. $A^T A$ is always invertible if A is invertible
Choose the correct answer from the options given below :

• A. A, B and C only
• B. A and B only
• C. A, B and D only
• D. A, B, C and D

Hint:

Remember: $det(A) = \text{Product of Eigenvalues}$. If any eigenvalue is zero, the determinant is zero, and the matrix is not invertible.

Answer 1

The Correct Option is C