Question

If $A = \begin{bmatrix} \alpha & 0 \\ 1 & 1 \end{bmatrix},B = \begin{bmatrix} 1 & 0 \\ 5 & 1 \end{bmatrix}$, then the value of $\alpha$for which

$A^{2} = B$ is

• A. 1
• B. ­ –1
• C. 4
• D. No real values

Answer 1

Answer: (D)

No real values

Answer 2

$A^{2} = \begin{bmatrix} \alpha & 0 \\ 1 & 1 \end{bmatrix}\begin{bmatrix} \alpha & 0 \\ 1 & 1 \end{bmatrix} = \begin{bmatrix} \alpha^{2} & 0 \\ \alpha + 1 & 1 \end{bmatrix}$∵ $A^{2} = B$ (given)

Then $\begin{bmatrix} \alpha^{2} & 0 \\ \alpha + 1 & 1 \end{bmatrix} = \begin{bmatrix} 1 & 0 \\ 5 & 1 \end{bmatrix}$⇒ $\alpha^{2} = 1$and $\alpha + 1 = 5$.

Clearly no real value of $\alpha$