If A = $\begin{bmatrix$}[r] 3 & 4 \ 0 & 1 \end{bmatrix} \text{ and } B = \begin{bmatrix}[r] 9 & 16 \ 0 & -x \end{bmatrix} such that A² = B, then the value of x is :

1. 4

2. -1

3. 1

4. -4

Given,

A² = B

$\Rightarrow \begin{bmatrix$}[r] 3 & 4 \ 0 & 1 \end{bmatrix}\begin{bmatrix}[r] 3 & 4 \ 0 & 1 \end{bmatrix} = \begin{bmatrix}[r] 9 & 16 \ 0 & -x \end{bmatrix} \\[1em] \Rightarrow \begin{bmatrix}[r] 3 \times 3 + 4 \times 0 & 3 \times 4 + 4 \times 1 \ 0 \times 3 + 1 \times 0 & 0 \times 4 + 1 \times 1 \end{bmatrix} = \begin{bmatrix}[r] 9 & 16 \ 0 & -x \end{bmatrix} \\[1em] \Rightarrow \begin{bmatrix}[r] 9 + 0 & 12 + 4 \ 0 + 0 & 0 + 1 \end{bmatrix} = \begin{bmatrix}[r] 9 & 16 \ 0 & -x \end{bmatrix} \\[1em] \Rightarrow \begin{bmatrix}[r] 9 & 16 \ 0 & 1 \end{bmatrix} = \begin{bmatrix}[r] 9 & 16 \ 0 & -x \end{bmatrix}

So,

⇒ -x = 1

⇒ x = -1.

Hence, Option 2 is the correct option.