If A is any square matrix of order 3 x 3 such that |A| = 3, then the value of |adj. A| is
A square matrix is a matrix with an equal number of rows and columns. It is denoted as an “n × n” matrix where “n” represents the number of rows and columns. Square matrices are essential in various operations like calculating determinants and finding matrix inverses.
Chapter 4 of Class 12 Maths focuses on Determinants. It explains how to calculate determinants using cofactor expansion and explores their properties. The chapter also covers applications like solving linear equations using Cramer’s rule and finding matrix inverses. These concepts are vital for students preparing for the CBSE Exam 2024-25.
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We are given that A is a square matrix of order 3×3 and |A| = 3. We have to find the value of |adj(A)|.
The relation between the determinant of a matrix A and the determinant of its adjoint adj(A) is given by the formula:
|adj(A)| = |A|^(n-1)
Here, n = 3 because A is a 3×3 matrix. So the formula becomes:
|adj(A)| = |A|^(3-1) = |A|²
Since |A| = 3, we calculate:
|adj(A)| = 3² = 9
Hence, the correct value of |adj(A)| is 9.
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