Matrices Test -...

If $$\displaystyle A=\begin{bmatrix} 1 & 0 \\ \cfrac { 1 }{ 2 }  & 1 \end{bmatrix},$$ then $${A}^{50}$$ is

If $$\displaystyle \left[ \begin{matrix} 1 & x & 1 \end{matrix} \right] \begin{bmatrix} 1 & 3 & 2 \\ 2 & 5 & 1 \\ 15 & 3 & 2 \end{bmatrix}\: \begin{bmatrix} 1 \\ 2 \\ x \end{bmatrix}=O$$ then $$x$$ is

If $$\displaystyle \begin{bmatrix} 2 & -3 \\ 1 & \lambda \end{bmatrix} \times  \begin{bmatrix} 1 & 5 & \mu \\ 0 & 2 & -3 \end{bmatrix} = \begin{bmatrix} 2 & 4 & 1 \\ 1 & -1 & 13 \end{bmatrix}$$ then

If $$\displaystyle A = \begin{bmatrix} 0 & c & -b \\ -c & 0 & a \\ b & -a & 0 \end{bmatrix}$$ and $$\displaystyle B = \begin{bmatrix} a^2 & ab & ac \\ ba & b^2 & bc \\ ca & cb & c^2 \end{bmatrix}$$ then $$AB$$ is equal to

If the matrix $$\displaystyle A = \begin{bmatrix} a & b \\ c & d \end{bmatrix}$$ then $$\displaystyle A^2$$ is

If $$A = \begin{bmatrix} 0 & 2 & 3 \\ 3 & 5 & 7 \end{bmatrix},$$ $$B = \begin{bmatrix} 1 & 3 & 7 \\ 2 & 4 & 1 \end{bmatrix}$$ and $$A+B = \begin{bmatrix} 1 & 5 & 10 \\ 5 & k & 8 \end{bmatrix},\\ $$ then find the value of $$k .$$

If $$\displaystyle A = \begin{bmatrix} 4 & -1 & -4 \\ 3 & 0 & -4 \\ 3 & -1 & -3 \end{bmatrix}$$ then $$\displaystyle A^2$$ is equal to

If $$A$$ be a matrix such that $$\displaystyle A \times  \begin{bmatrix} 1 & -2 \\ 1 & 4 \end{bmatrix} = \begin{bmatrix} 6 & 0 \\ 0 & 6 \end{bmatrix}$$ then $$A$$ is

If $$\displaystyle \begin{bmatrix} x+y & y \\ 2x & x-y \end{bmatrix} \: \begin{bmatrix} 2 \\ -2 \end{bmatrix} = \begin{bmatrix} 3 \\ 2 \end{bmatrix}$$ then $$x-y$$ is equal to

If $$A = \begin{pmatrix}1& 2 & 2 \\ 2 & 1 & 2 \\ 2 & 2 & 1\end{pmatrix}$$

If  $$A^2 - 4A =pI $$ where $$I$$ and $$O$$ are the unit matrix and the null matrix of order $$3$$ respectively. Find the value of $$p$$