Class CBSE Class 12 Mathematics Matrices and Determinants Q #851
KNOWLEDGE BASED
APPLY
1 Marks 2023 MCQ SINGLE
Let A be a 3\times3 matrix such that | adj A|=64. Then |A| is equal to:
(A) 8 only
(B) \- 8 only
(C) 64
(D) 8 or-8
Prev Next

AI Tutor Explanation

Powered by Gemini

Step-by-Step Solution

We are given that |adj A| = 64, where A is a 3x3 matrix.

We know that for a square matrix A of order n, |adj A| = |A|^(n-1).

In this case, n = 3, so |adj A| = |A|^(3-1) = |A|^2.

Therefore, |A|^2 = 64.

Taking the square root of both sides, we get |A| = ±√64 = ±8.

So, |A| = 8 or |A| = -8.

Correct Answer: 8 or -8

AI Suggestion: Option D

AI generated content. Review strictly for academic accuracy.

Pedagogical Audit
Bloom's Analysis: This is an APPLY question because the student needs to apply the formula relating |adj A| and |A| to find the value of |A|.
Knowledge Dimension: PROCEDURAL
Justification: The question requires the student to follow a specific procedure or algorithm to solve the problem, which involves using the relationship between the determinant of a matrix and the determinant of its adjoint.
Syllabus Audit: In the context of CBSE Class 12, this is classified as KNOWLEDGE. The question directly tests the student's knowledge of a specific formula and its application.

More from this Chapter

MCQ_SINGLE
The matrix \(A=\begin{bmatrix}\sqrt{3}&0&0\\ 0&\sqrt{2}&0\\ 0&0&\sqrt{5}\end{bmatrix}\) is a/an:
MCQ_SINGLE
Let A be the area of a triangle having vertices $(x_1, y_1), (x_2, y_2)$ and $(x_3, y_3)$. Which of the following is correct?
MCQ_SINGLE
If $A=\begin{bmatrix}1&4&x\\ z&2&y\\ -3&-1&3\end{bmatrix}$ is a symmetric matrix, then the value of $x+y+z$ is :
MCQ_SINGLE
If \(A=[a_{ij}]\) is an identity matrix, then which of the following is true ?
MCQ_SINGLE
If A=[(1, 0), (2, 1)], B=[(x, 0), (1, 1)] and A=B², then x equals
View All Questions