If $\begin{bmatrix} 0 & x \\ 2 & 1 \end{bmatrix} + 2\begin{bmatrix} 3 & 1 \\ y & 0 \end{bmatrix} = \begin{bmatrix} 6 & 5 \\ 8 & 1 \end{bmatrix}$, then the value of $2x+3y$ is :

Let $A$ and $B$ be two symmetric matrices of same order, then

Match List-I with List-II

Choose the correct answer from the options given below:

If $a, b$ and $c$ are non-zero real number such that $\begin{vmatrix} 1+a & 1 & 1 \\ 1 & 1+b & 1 \\ 1 & 1 & 1+c \end{vmatrix} = 0$, then value of $\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c}$ is

If $A = \begin{bmatrix} -2 & 6 \\ -5 & -1 \end{bmatrix}$ then $A^{-1}$ is :

The number of all possible matrices of order $3 \times 3$ with each entry $-1, 0$ or $1$ is

Let $A = \begin{bmatrix} \cos\theta & -\sin\theta \\ \sin\theta & \cos\theta \end{bmatrix}$, then $(A^{-1})^T$ equals

If matrix $A = \begin{bmatrix} 2 & 3 \\ 1 & 2 \end{bmatrix}$, then $A^2+I$ is equal to: (Where I is an identity matrix of order 2)