Matrices Test -...

If $\displaystyle A=\left[ \begin{matrix} 3 & 1 \\ -1 & 2 \end{matrix} \right]$ and $\displaystyle I=\left[ \begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix} \right]$, then the correct statement is:

If AB = AC then 

If $\mathrm{A}^{2}=\mathrm{A},\ \mathrm{B}^{2}=\mathrm{B},\ \mathrm{A}\mathrm{B}=\mathrm{B}\mathrm{A}=O$ (Null Matrix), then $(\mathrm{A}+\mathrm{B})^{2}=$

$I$ $$A=\left[\begin{array}{ll}
0 & 1\\ 1 & 0 \end{array}\right]$,$A^{4}=$$
($I$ is an identity matrix.)

lf $$\mathrm{A}= \left[\begin{array}{lll}
o & c & -b\\
-c & o & a\\
b & -a & o
\end{array}\right]\mathrm{a}\mathrm{n}\mathrm{d}$$ \mathrm{B}=\left[\begin{array}{lll}
a^{2} & ab & ac\\
ab & b^{2} & bc\\
ac & bc & c^{2}
\end{array}\right],$then$\mathrm{A}\mathrm{B}=$$

lIf $$\mathrm{A} =\left[\begin{array}{ll}
a & 0\\
a & 0
\end{array}\right],\ \mathrm{B}=\left[\begin{array}{ll}
0 & 0\\
b & b
\end{array}\right],$then$\mathrm{A}\mathrm{B}=$$ 

If $$A=\left[\begin{array}{lll}
1 & -2 & 3\\
-4 & 2 & 5
\end{array}\right]$and$B=\left[\begin{array}{ll}
2 & 3\\
4 & 5\\
2 & 1
\end{array}\right],$$ then 

$A=\left[\begin{array}{lll} 0 & 1 & -2\\1 & 0 & 3\\2 &-3 & 0 \end{array}\right]$ then $\mathrm{A}+\mathrm{A}^{\mathrm{T}}=$

$$\left[\begin{array}{ll}
x & 0\\
0 & y
\end{array}\right]\left[\begin{array}{ll}
a & b\\
c & d
\end{array}\right]=$$

If $$\mathrm{A}=\left[\begin{array}{lll}
1 & -3 & -4\\
-1 & 3 & 4\\
1 & -3 & -4
\end{array}\right]$, then$\mathrm{A}^{2}=$$