If A is any square matrix of order 2 x 2 such that |A| = -7, then the value of |adj. A| is
A square matrix is a matrix with an equal number of rows and columns. The order of a square matrix refers to its size, represented as “n x n,” where “n” is the number of rows (or columns). Examples include 2×2, 3×3, 4×4 matrices, and so on.
Class 12 Maths Chapter 4 focuses on Determinants. It covers properties of determinants such as addition subtraction multiplication of determinants along with cofactor expansion method. The chapter also includes applications like finding the area of a triangle solving systems of linear equations using Cramer’s rule and understanding the inverse of a matrix. This is crucial for CBSE Exam 2024-25.
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For any square matrix A of order n, the determinant of its adjugate is given by:
|adj A| = |A|^(n − 1)
For a 2×2 matrix (n = 2):
|adj A| = |A|^(2 − 1) = |A|
Given |A| = −7, we have:
|adj A| = −7
Thus, the correct answer is −7.
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