1.2 Inverse of a Non-Singular Square Matrix
Chapter 1: Chapter 1 · MATHEMATICS-VOLUME 1 · EN medium
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We recall that a square matrix is called a non-singular matrix if its determinant is not equal to zero and a square matrix is called singular if its determinant is zero. We have already learnt about multiplication of a matrix by a scalar, addition of two matrices, and multiplication of two matrices. But a rule could not be formulated to perform division of a matrix by another matrix since a matrix is just an arrangement of numbers and has no numerical value. When we say that, a matrix A is of order n , we mean that A is a square matrix having n rows and n columns. In the case of a real number x ¹ , there exists a real number say called the inverse (or reciprocal) of x such that xy yx = .
📖 Class 12 Mathematics English Volume 1 2025 Edition www.tntextbooks.in · Page 10
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We recall that a square matrix is called a non-singular matrix if its determinant is not equal to zero and a square matrix is called singular if its determinant is zero. We have already learnt about multiplication of a matrix by a scalar, addition of two matrices, and multiplication of two matrices. But a rule could not be formulated to perform division of a matrix by another matrix since a matrix is just an arrangement of numbers and has no numerical value. When we say that, a matrix A is of order n , we mean that A is a square matrix having n rows and n columns.
In the case of a real number x ¹ , there exists a real number say called the inverse (or reciprocal) of x such that xy yx = . In the same line of thinking, when a matrix A is given, we search for a matrix B such that the products AB and BA can be found and AB
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