Matrices Test -...

If $$\begin{bmatrix} x & 1 \\ 1 & 0 \end{bmatrix}$$ and $$  A^{2}=I$$, then $$x=$$

If $$[1\ 2\ 3] B = [3\ 4],$$ then order of the matrix $$B$$ is

The inverse of the matrix $$\begin{bmatrix}2 & 1\\ 1 & 3\end{bmatrix}$$ is

If $$A = \begin{bmatrix}1 & -2 & 3\\ -4 & 2 & 5\end{bmatrix}$$ and $$B = \begin{bmatrix}2 & 3\\ 4 & 5\\ 2 & 1\end{bmatrix}$$, then  the product  of AB and BA is

Let A be a square matrix. Which of the following is/are not symmetric matrix/matrices?

If $$A = \begin{bmatrix}1 & 2 & 2\\ 2 & 1 & -2\\ a & 2 & b\end{bmatrix}$$ is a matrix satisfying $$AA^T = 9 I_3$$, then the values of $$a$$ and $$b$$ are

Using elementary transformation, find the inverse of the matrix $$A =\begin{bmatrix}a & b\\ c & \left ( \frac{1 + bc}{a} \right )\end{bmatrix}$$.

The value of x is such that matrix product $$\begin{bmatrix}2 & 0 & 7\\ 0 & 1 & 0\\ 1 & -2 & 1\end{bmatrix} \begin{bmatrix}-x & 14x & 7x\\ 0 & 1 & 0\\ x & -4x & -2x\end{bmatrix}$$ equals an identity matrix. Then the value of 20x is

Given $$A, B, C$$ are three matrices such that 
$$A = \begin{bmatrix}x & y & z\end{bmatrix}$$, $$B = \begin{bmatrix} a  & h & g \\ h & b & f \\ g & f & c\end{bmatrix}$$, $$C = \begin{bmatrix}x \\ y \\ z\end{bmatrix}.$$ Evaluate $$ABC$$.

If $$A = \begin{bmatrix} 1 & -2 & 3 \\ -4 & 2 & 5 \end{bmatrix}$$ and $$B = \begin{bmatrix} 2 & 3 \\ 4 & 5 \\ 2 & 1 \end{bmatrix}$$. Find $$AB$$ and show that $$AB \ne BA$$