If $A = \begin{bmatrix} 1 & 1 \\ 0 & 1 \end{bmatrix}$, then the value of $A^{20}$ is:

The value of the expression $\frac{x^2 + y^2}{x - y}$ is:

If A and B are symmetric matrices of the same order then which of the following statements are correct?

A. AB is symmetric matrix

B. AB - BA is skew symmetric matrix

C. $B^TAB$ is symmetric matrix

D. $A - A^T$ is skew symmetric matrix

Choose the correct answer from the options given below:

If $y = -4$ is a root of $\begin{vmatrix} y & 2 & 3 \\ 1 & y & 1 \\ 3 & 2 & y \end{vmatrix} = 0$, then the product of the other two roots is

Let $A = \begin{bmatrix} 152 & 105 & 3 \\ 149 & 25 & 35 \\ 2 & 1 & 0 \end{bmatrix}$. If $A_{ij}$ denotes the co-factor of an element $a_{ij}$ of the matrix A, then the value of $a_{11}A_{21} + a_{12}A_{22} + a_{13}A_{23}$ is equal to

Match List - I with List - II.

Choose the correct answer from the options given below :

If $A = \begin{bmatrix} x & -3 & 4 \\ 3 & y & -5\\-4&z&0 \end{bmatrix}$ is a Skew-Symmetric matrix and $adj \ A = [a_{ij}]_{3 \times3}$, then $a_{11} + a_{22} + a_{33}$ is equal to