A square matrix is a matrix with an equal number of rows and columns. It is represented as an “n × n” matrix where “n” is the number of rows and columns. Square matrices are essential in linear algebra and are used in various operations like finding determinants and inverses.
Chapter 4 of Class 12 Maths is about Determinants. It covers properties and methods for calculating determinants such as cofactor expansion and adjoint method. The chapter also explains the applications of determinants in solving linear equations using Cramer’s rule and finding the inverse of matrices. Understanding these concepts is essential for the CBSE Exam 2024-25.
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We are given that A is a square matrix of order 3 and |A| = -4. We are asked to find the value of |adj(A)|.
The formula for the determinant of the adjugate matrix adj(A) for a square matrix A of order n is
|adj(A)| = |A|^(n-1)
For a matrix of order 3, n = 3. Hence, the above formula becomes
|adj(A)| = |A|^(3-1) = |A|²
We know that |A| = -4. So,
|adj(A)| = (-4)² = 16
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