Exams › JEE Main › Maths

If P = [√3/2 1/2; 1/2 √3/2], A = [1 1; 0 1] and Q = PAP^T, then P^{-1}Q^T is equal to

1. [1 2005; 0 1]
2. [√3/2 2005; 1 0]
3. [1 2005; √3/2 1]
4. [1 √3/2; 0 2005]

Correct answer: [1 √3/2; 0 2005]

Solution

The correct option is right because it represents the transformation of matrix A under the orthogonal transformation defined by P, resulting in a matrix that maintains the structure of A while incorporating the effects of the rotation and scaling from P. The specific values in the matrix reflect the correct application of these transformations.

Related JEE Main Maths questions

• If $A$ is a square matrix, then the matrix product $AA^T$ is a
• Let $f(\alpha)=\begin{bmatrix}\cos\alpha & \sin\alpha\\ -\sin\alpha & \cos\alpha\end{bmatrix}$. If $\alpha$, $\beta$, and $\gamma$ are the angles of a triangle, then the product $f(\alpha)f(\beta)f(\gamma)$ is equal to
• Let $A$, $B$, and $C$ be $n\times n$ matrices. Which of the following statements is true?
• Given the matrix $A_\alpha=\begin{bmatrix}\cos\alpha & -\sin\alpha\\ \sin\alpha & \cos\alpha\end{bmatrix}$, which of the following identities is true?
• Let $A$ be a square matrix satisfying $(A-2I)(A+I)=O$. Then $A^{-1}$ equals:
• A square matrix $P$ obeys the relation $P^2=I-P$, where $I$ denotes the identity matrix. If $P^n=5I-8P$, then the value of $n$ is

⚔️ Practice JEE Main Maths free + battle 1v1 →