Matrix A = $\begin{bmatrix$}[r] 2 & -2\ -2 & 0 \end{bmatrix} and matrix B = $\begin{bmatrix$}[r] 5 & 5\ 5 & 5 \end{bmatrix}

Statement 1 : AB = 0

Statement 2 : AB = 0, even if A ≠ 0 and B ≠ 0.

1. Both the statements are true.

2. Both the statements are false.

3. Statement 1 is true, and statement 2 is false.

4. Statement 1 is false, and statement 2 is true.

Find x and y, if :

$\begin{bmatrix$}[r] 3 & -2 \ -1 & 4 \end{bmatrix}\begin{bmatrix}[r] 2x \ 1 \end{bmatrix} + 2\begin{bmatrix}[r] -4 \ 5 \end{bmatrix} = 4\begin{bmatrix}[r] 2 \ y \end{bmatrix}

If $\begin{bmatrix$}[r] x & y \end{bmatrix}\begin{bmatrix}[r] x \ y \end{bmatrix} = \begin{bmatrix}[r] 25 \end{bmatrix} \text{ and } \begin{bmatrix}[r] -x & y \end{bmatrix}\begin{bmatrix}[r] 2x \ y \end{bmatrix} = \begin{bmatrix}[r] -2 \end{bmatrix};

find x and y, if :

(i) x, y ∈ W (whole numbers)

(ii) x, y ∈ Z (integers)

Evaluate :

$\begin{bmatrix$}[r] cos 45° & sin 30° \ \sqrt{2}cos 0° & sin 0° \end{bmatrix}\begin{bmatrix}[r] sin 45° & cos 90° \ sin 90° & cot 45° \end{bmatrix}