If A is any square matrix of order 3 x 3 such that |adj. A| = 25 and |A| is non-positive, then the value of |A| is
The adjoint of a matrix is the transpose of its cofactor matrix. It is denoted as adj(A) and is used to find the inverse of a matrix. The adjoint is essential in solving systems of linear equations and matrix operations. It helps in calculating the inverse using the formula A⁻¹ = adj(A)/det(A).
Chapter 4 of Class 12 Maths is about Determinants. It explains the calculation of determinants using methods like cofactor expansion and discusses their properties. The chapter also covers applications such as solving linear equations using Cramer’s rule and finding the inverse of matrices. These concepts are important for the CBSE Exam 2024-25.
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We are given that A is a square matrix of order 3×3 and |adj(A)| = 25. We need to find the value of |A|.
The formula for the relation between the determinant of a matrix A and its adjoint is given as under:
|adj(A)| = |A|(n -1), where n is the order of the given matrix.
When n = 3 for 3×3 matrix, it becomes:
|adj(A)| = |A|²
We are given that |adj(A)| = 25.
|A|² = 25
We find the square root of both sides of the equation
|A| = ±5
Since we know that |A| is non-positive we choose negative sign
|A| = -5
So, the correct answer is -5.
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