Question

Choose the correct answer in the following question s: If is such that then A. B. C. D.

Answer 1

Given the value of matrix A is,

A=[ α β γ −α ]

Given that square of matrix A is,

A 2 =I A⋅A=I [ α β γ −α ][ α β γ −α ]=[ 1 0 0 1 ] [ α⋅α+β⋅γ α⋅β+β( −α ) γ⋅α−α⋅γ γ⋅β+( −α )( −α ) ]=[ 1 0 0 1 ]

Further simplify the above matrices,

[ α 2 +β⋅γ 0 0 β⋅γ+ α 2 ]=[ 1 0 0 1 ]

Compare the corresponding elements of the above matrices.

α 2 +βγ=1 1− α 2 −βγ=0

Thus, out of all the four options, option (C) is correct.