If the square of the matrix $\begin{bmatrix} \alpha & \beta \\ \gamma & -\alpha \end{bmatrix}$ is the unit matrix of order $2$, then $\alpha, \beta$ and $\gamma$ should satisfy the relation. (1) $1 + \alpha^2 + \beta\gamma = 0$ (2) $1 - \alpha^2 - \beta\gamma = 0$ (3) $1 - \alpha^2 + \beta\gamma = 0$ (4) $1 + \alpha^2 - \beta\gamma = 0$

If the square of the matrix α β ; gamma -α is the unit matrix of order 2, then α, β and γ should satisfy the r

Exercise 7.5 · Q14

\begin{bmatrix} \alpha & \beta \\ \gamma & -\alpha \end{bmatrix}

(1)

1 + \alpha^2 + \beta\gamma = 0

(2)

1 - \alpha^2 - \beta\gamma = 0

(3)

1 - \alpha^2 + \beta\gamma = 0

(4)

1 + \alpha^2 - \beta\gamma = 0

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Compute the square of the $2\times2$ matrix and match $I$ .

This tests matrix squaring and the identity condition.

Step 1. With $M = \begin{bmatrix} \alpha & \beta \\ \gamma & -\alpha \end{bmatrix}$ , top-left of $M^2 = \alpha^2 + \beta\gamma$ ; top-right $= \alpha\beta - \beta\alpha = 0$ . …

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Q.If the square of the matrix $\begin{bmatrix} \alpha & \beta \\ \gamma & -\alpha \end{bmatrix}$ is the unit matrix of order $2$ , then $\alpha, \beta$ and $\gamma$ should satisfy the relation.

Concept understanding — Properties of Matrix Addition, Scalar Multiplication and Product of Matrices

Q.If the square of the matrix [αβγ−α]\begin{bmatrix} \alpha & \beta \\ \gamma & -\alpha \end{bmatrix}[αγ​β−α​] is the unit matrix of order 222, then α,β\alpha, \betaα,β and γ\gammaγ should satisfy the relation.

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Q.If the square of the matrix $\begin{bmatrix} \alpha & \beta \\ \gamma & -\alpha \end{bmatrix}$ is the unit matrix of order $2$ , then $\alpha, \beta$ and $\gamma$ should satisfy the relation.

Unlock everything free for 14 days