Matrices Test -...

If $$O\left( A \right) =2\times 3,$$ $$O\left( B \right) =3\times 2$$ and $$O\left( C \right) =3\times 3$$, which one of the following is not defined?

If $$A=
\begin{bmatrix}
2 & -1 \\
-1 & 2
\end{bmatrix}$$ and $$I$$ is the unit matrix of order $$2$$, then $$A^2$$equals

Let $$A=\begin{bmatrix} 3 & 1\\ -1 & 2\end{bmatrix}$$, then

Let $$A=\begin{bmatrix} 1 & -1 & 1 \\ 2 & 1 & -3 \\ 1 & 1 & 1 \end{bmatrix}$$ and $$10B=\begin{bmatrix} 4 & 2 & 2 \\ -5 & 0 & \alpha  \\ 1 & -2 & 3 \end{bmatrix}$$. If $$B$$ is the inverse of matrix $$A$$, then $$\alpha $$ is

$$If\quad A=\begin{bmatrix} ab & { b }^{ 2 } \\ -{ a }^{ 2 } & -ab \end{bmatrix},then\quad { A }^{ 2 }\quad is\quad equal\quad to$$

If $$\left[ \begin{matrix} x & 4 & -1 \end{matrix} \right] \left[ \begin{matrix} 2 & 1 & 0 \\ 1 & 0 & 2 \\ 0 & 2 & 4 \end{matrix} \right] \left[ \begin{matrix} x \\ 4 \\ -1 \end{matrix} \right] =0,$$ then $$x=$$

The value of $$x$$, so that $$\left[ 1 \quad x \quad 1 \right] \begin{bmatrix} 1 & 3 & 2 \\ 0 & 5 & 1 \\ 0 & 3 & 2 \end{bmatrix}\begin{bmatrix} 1 \\ 1 \\ x \end{bmatrix}=0$$ is/are

If the matrix $$\begin{bmatrix} 0 & 2\beta & \Upsilon \\ \alpha & \beta & -\Upsilon \\ \alpha & -\beta & \Upsilon \end{bmatrix}$$is orthogonal, then

If $$A=\begin{bmatrix} 3 & -3 & 4 \\ 2 & -3 & 4 \\ 0 & -1 & 1 \end{bmatrix}$$, then : $$A^{-1}$$=

If $$A=\left[ \begin{matrix} 1 & 2 & 2 \\ 2 & 1 & 2 \\ 2 & 2 & 1 \end{matrix} \right] $$, then $$A^{2}-4\ A$$ is equal to