Two matrices A and B each of order 2 x 2.

Assertion (A) : A X B = 0 ⇒ A = 0 or B = 0.

Reason (R) : Let $A = \begin{bmatrix$}[r] 2 & 2 \ 5 & 5 \end{bmatrix} ≠ 0 and $B = \begin{bmatrix$}[r] -4 & 3 \ 4 & -3 \end{bmatrix} ≠ 0 but A x B = $\begin{bmatrix$}[r] 2 & 2 \ 5 & 5 \end{bmatrix}\begin{bmatrix}[r] -4 & 3 \ 4 & -3 \end{bmatrix} = 0.

1. A is true, R is false.

2. A is false, R is true.

3. Both A and R are true and R is correct reason for A.

4. Both A and R are true and R is incorrect reason for A.

Matrix A = $\begin{bmatrix$}[r] x & y \end{bmatrix} and Matrix B = $\begin{bmatrix$}[r] a \ b \end{bmatrix}.

Assertion (A) : Product BA is possible and order of resulting matrix is 2 x 2.

Reason (R) : The product BA of two matrices A and B is possible only if number of rows in matrix B Is same as number of columns in matrix A.

1. A is true, R is false.

2. A is false, R is true.

3. Both A and R are true and R is correct reason for A.

4. Both A and R are true and R is incorrect reason for A.

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}