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
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
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
Show Hint
Inverse of product reverses order.
Updated On: Mar 17, 2026
- M(β)M(α)
- M(-α)M(-β)
- M(-β)M(-α)
- -M(β)M(α)
Show Solution
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The Correct Option is C
Solution and Explanation
For orthogonal matrices:
M⁻¹(θ)=M(-θ)
Also:
(AB)⁻¹=B⁻¹A⁻¹
Hence:
[M(α)M(β)]⁻¹=M(-β)M(-α)
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