MCA Entrance Previous Year Question Bank

Assertion: $ A(BA) $ and $ (AB)A $ are symmetric matrices.

Reason: $ AB $ is symmetric matrix, if matrix multiplication of $ A $ with $ B $ is commutation.

$ S $ and $ T $ are symmetric matrices of the same order, then which of the following statements are true?

(A) $ S + T $ is a symmetric matrix

(B) $ ST - TS $ is a skew-symmetric matrix

(C) $ ST + TS $ is a symmetric matrix

(D) $ ST - TS $ is a symmetric matrix

If $ A=\begin{pmatrix} a & b \\ b & a \end{pmatrix} \ \text{and} \ A^2=\begin{pmatrix} \alpha & \beta \\ \beta & \alpha \end{pmatrix} $

Which of the following statements are TRUE?

(A) If each element in a row is a constant multipilier of corresponding element of another row of a determinant, then the value of the determinant is always non-zero.

(B) If each element on one side of the principal diagonal of a determinant is zero, than the value of the determinant is the product of the diagonal elements.

(C) The value of determinant of skew symmetric matrix of odd order is always non-zero.

(D) If A is a non-singular matrix of order three, the |adj A| = |A|²

Choose the correct answer from the options given below

Select a suitable figure from the given options that would complete the figure matrix?