COMEDK · Maths · 21. Matrices
If \(A(t)=\left[\begin{array}{cc}\cos t & \sin t \\ -\sin t & \cos t\end{array}\right]\) then the product of \(A(t)\) and \(A(-t)\) is
- A \(A^2(-t)\)
- B Identity matrix
- C \(A^2(t)\)
- D Null matrix
Answer & Solution
Correct Answer
(B) Identity matrix
Step-by-step Solution
Detailed explanation
Given \(A(t) = \begin{bmatrix} \cos t & \sin t \\ -\sin t & \cos t \end{bmatrix}\). Then \(A(-t) = \begin{bmatrix} \cos(-t) & \sin(-t) \\ -\sin(-t) & \cos(-t) \end{bmatrix} = \begin{bmatrix} \cos t & -\sin t \\ \sin t & \cos t \end{bmatrix}\). The product \(A(t)A(-t)\) is…
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