Matrices Test -...

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

If $$\displaystyle A=\begin{bmatrix} 1 & \frac { 1 }{ 2 }  \\ 0 & 1 \end{bmatrix}$$ then $${ A }^{ 64 }$$ is

Find the value of $$x$$ and $$y$$ that satisfy the equation:
$$\begin{bmatrix} 3&-2 \\3  &0 \\2 &4 \end{bmatrix}
\begin{bmatrix} y&y \\x &x \end{bmatrix}=\begin{bmatrix} 3&3 \\3y  &3y \\10 &10 \end{bmatrix}$$

Let $$A$$ be square matrix. Then which of the following is not a symmetric matrix.

If A is any square matrix then (1/2) $$\displaystyle \left ( A+A^{T} \right )$$ is a _____ matrix

If $$A=\begin{bmatrix} 4 & 2 \\ -1 & 1 \end{bmatrix}$$, then $$(A-2I)(A-3I)=$$ 

Inverse of a diagonal matrix is

If $$A+I=\begin{bmatrix} 3 & -2 \\ 4 & 1 \end{bmatrix}$$, then $$\left( A+I \right) \cdot \left( A-I \right) $$ is equal to

Two matrices $$A$$ and $$B$$ are multiplied to get $$AB$$ if

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