Which of the following statements are NOT TRUE?
(A) If \( A \) and \( B \) are symmetric matrices, then \( A B-B A \) is a skew symmetric matrix. (B) Multiplying a determinant by k means multiply elements of one column by k . (C) If \( \mathrm{A}^{2}-\mathrm{A}+\mathrm{I}=0 \) , then \( \mathrm{A}^{-1} \) is equal to \( \mathrm{A}+\mathrm{I} \) . (D) If A and \( B \) are invertible matrices of same order, then \( (A+B)^{-1}=B^{-1}+A^{-1} \) . Choose the correct answer from the options given below:
(A)
If \( A \) and \( B \) are symmetric, then \( AB - BA \) is skew-symmetric.
True (since \((AB - BA)^T = BA - AB = -(AB - BA)\)).
(B)
"Multiplying a determinant by \( k \) means multiply elements of one column by \( k \)."
False (correct interpretation: multiplying one column by \( k \) multiplies the determinant by \( k \), not the other way around).
(C)
If \( A^2 - A + I = 0 \), then \( A^{-1} = A + I \).
False (correct inverse: \( A^{-1} = I - A \), since \( A(I - A) = A - A^2 = I \)).
(D)
If \( A \) and \( B \) are invertible, then \( (A + B)^{-1} = B^{-1} + A^{-1} \).
False (matrix addition does not distribute like this over inverses).
Final Answer:
Only (B), (C), and (D) are NOT TRUE.
Reinforce your conceptual grasp with related questions from CUET-MCA 2024:
Take timed full-length mock tests with authentic question distributions, negative marking (+12/-3 in Math), and instant All India Rank calculation.
Start Free Mock Test Series →