Question

If M(α)= bmatrix α & -α & 0
α & α & 0
0 & 0 & 1 bmatrix, M(β)= bmatrix β & 0 & β
0 & 1 & 0
-β & 0 & β bmatrix then [M(α)M(β)]^-1 is equal to

• A. M(β)M(α)
• B. M(-α)M(-β)
• C. M(-β)M(-α)
• D. -M(β)M(α)

Hint:

Inverse of product reverses order.

Answer 1

The Correct Option is C

For orthogonal matrices: M⁻¹(θ)=M(-θ) Also: (AB)⁻¹=B⁻¹A⁻¹ Hence: [M(α)M(β)]⁻¹=M(-β)M(-α)