"If for the matrix, $$A = \left[ {\matrix{ 1 & { - \alpha } \cr \alpha & \beta \cr } } \right]$$, $A{A^T} = {I_2}$, then the value of ${\alpha ^4} + {\beta ^4}$ is :"

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Accepted Answer

"$$\left[ {\matrix{ 1 & { - \alpha } \cr \alpha & \beta \cr } } \right]\left[ {\matrix{ 1 & \alpha \cr { - \alpha } & \beta \cr } } \right] = \left[ {\matrix{ {1 + {\alpha ^2}} & {\alpha - \alpha \beta } \cr {\alpha - \alpha \beta } & {{\alpha ^2} + {\beta ^2}} \cr } } \right] = \left[ {\matrix{ 1 & 0 \cr 0 & 1 \cr } } \right]$$

1 + $\alpha$² = 1

$\alpha$² = 0

$\alpha$² + $\beta$² = 1

$\beta$² = 1

$\alpha$⁴ = 0

$\beta$⁴ = 1

$\alpha$⁴ + $\beta$⁴ = 1"

If for the matrix, $$A = \left[ {\matrix{ 1 & { - \alpha } \cr \alpha & \beta \cr } } \right]$$, $A{A^T} = {I_2}$, then the value of ${\alpha ^4} + {\beta ^4}$ is :

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If for the matrix, $$A = \left[ {\matrix{ 1 & { - \alpha } \cr \alpha & \beta \cr } } \right]$$, $A{A^T} = {I_2}$, then the value of ${\alpha ^4} + {\beta ^4}$ is :

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