Matrices Test -...

If $$\mathrm{A}=\left[\begin{array}{ll}
0 & 1\\
1 & 0
\end{array}\right]$$, then $$\mathrm{A}^{5}=$$

If $$\mathrm{A}=\left[\begin{array}{ll}
1 & 2\\
0 & 3
\end{array}\right]$$ and $$\mathrm{B}=[3 \space-1]$$, then $$\mathrm{B}\mathrm{A}=$$

$$ If \space A= \begin{bmatrix} a & h & g \\ h & b & f \\ g & f & c \end{bmatrix}$$, then A is 

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

lf $$\mathrm{A}=\left[\begin{array}{ll}
2 & -1\\
3 & -2
\end{array}\right],$$ then $$\mathrm{A}^{5}=$$

$$L=\left[\begin{array}{lll}
2 & 3 & 5\\
4 & 1 & 2\\
1 & 2 & 1
\end{array}\right] =P+Q$$, $$P$$  is a symmetric matrix, $${Q}$$ is a skew-symmetric matrix then $${P}$$ is equal to

 If  $$I=\begin{bmatrix}
1 & 0\\
0 & 1
\end{bmatrix}$$ and E =$$\begin{bmatrix}
0 & 1\\
0 & 0
\end{bmatrix}$$, then $$\left ( 2I+3E \right )^{3}=$$ 

If in a square matrix $$A=\left[ { a }_{ ij } \right] $$, we find that $${ a }_{ ij }={ a }_{ ji }\quad \forall \quad i,j$$ , then $$A$$ is

If P = $$ \begin{bmatrix}
1\\
3\\

4\end{bmatrix}$$ , Q = $$\begin{bmatrix}
2 & -1&5
\end{bmatrix}$$ then PQ = 

$$\mathrm{A}$$: If $$\mathrm{A}=\left\{\begin{array}{ll}
1 & -1\\
-1 & 1
\end{array}\right\} $$ and $$\mathrm{B}=\left\{\begin{array}{ll}
2 & 2\\
2 & 2
\end{array}\right\},$$ then $$\mathrm{A}\mathrm{B}=0$$ 
$$\mathrm{R}$$: If $$\mathrm{A}\mathrm{B}=0\Rightarrow  \mathrm{A}$$ or $$\mathrm{B}$$ need not be null matrices.