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Question: If A = \(\begin{bmatrix} \alpha & 0 \\ 1 & 1 \end{bmatrix}\) and B = \(\begin{bmatrix} 1 & 0 \\ 5 & ...

If A = [α011]\begin{bmatrix} \alpha & 0 \\ 1 & 1 \end{bmatrix} and B = [1051]\begin{bmatrix} 1 & 0 \\ 5 & 1 \end{bmatrix} such that A2 = B then a is

A

1

B

–1

C

4

D

None of these

Answer

None of these

Explanation

Solution

[α011]\begin{bmatrix} \alpha & 0 \\ 1 & 1 \end{bmatrix} = [1051]\begin{bmatrix} 1 & 0 \\ 5 & 1 \end{bmatrix}

Ž [α20α+11]\begin{bmatrix} \alpha^{2} & 0 \\ \alpha + 1 & 1 \end{bmatrix} = [1051]\begin{bmatrix} 1 & 0 \\ 5 & 1 \end{bmatrix}

Ž a2 = 1a + 1 = 5

Ž a = +1, – 1

satisfying a = 4 (AB surd )