If [α&β γ&-α] is square root of identity matrix of order 2 then

Question

If [α&β &gamma;&-α] is square root of identity matrix of order 2 then (A)  1 + α2 + β &gamma; = 0 (B)  1 + α2 - β &gamma; = 0 (C)  1 - α2 + β &gamma; = 0 (D) α2 + β &gamma; = 1

Tardigrade Admin · Accepted Answer

[α&β &gamma;&-α] = √I2 ; [α&β &gamma;&-α] [α &β &gamma; &-α ] = [1&0 0&1] ⇒ α2 + β&gamma; = 1

Q. If $[α γ β - α]$ is square root of identity matrix of order $2$ then

$1 + α^{2} + β γ = 0$

$1 + α^{2} - β γ = 0$

$1 - α^{2} + β γ = 0$

$α^{2} + β γ = 1$

$[α γ β - α] = I_{2};$
$[α γ β - α] [α γ β - α] = [1001]$
$\Rightarrow α^{2} + β γ = 1$

Q. If [αγ​β−α​] is square root of identity matrix of order 2 then

1+α2+βγ=0

1+α2−βγ=0

1−α2+βγ=0

α2+βγ=1