Exams › JEE Main › Maths

For a 2 × 2 matrix A, consider the following statements: Statement I: adj(adj A) = A Statement II: |adj A| = |A| Which of the following is correct?

1. Statement I is true, Statement II is true, and Statement II correctly explains Statement I.
2. Statement I is true, Statement II is false.
3. Statement I is false, Statement II is true.
4. Statement I is true, Statement II is true, but Statement II does not correctly explain Statement I.

Correct answer: Statement I is true, Statement II is true, and Statement II correctly explains Statement I.

Solution

Statement I is true because the adjugate of the adjugate of a matrix returns the original matrix for a 2x2 matrix. Statement II is also true as the determinant of the adjugate of a matrix equals the determinant of the original matrix, thus providing a valid explanation for Statement I.

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 →