👉 The IMA (Inverse Matrix Algebra) is a branch of mathematics that deals with the manipulation and properties of matrices, particularly focusing on invertible matrices and their inverses. It provides a systematic approach to solving systems of linear equations, performing matrix transformations, and understanding the geometric implications of matrix operations. Central to IMA is the concept that every square matrix \( A \) with entries from a field (like real or complex numbers) has an inverse \( A^{-1} \), provided \( A \) is non-singular (i.e., its determinant is non-zero). This inverse can be used to solve \( Ax = b \) for \( x \) by multiplying both sides by \( A^{-1} \), yielding \( x = A^{-1}b \). IMA also explores the properties of matrix multiplication, determinants, and eigenvalues, offering a robust framework for linear algebra applications in various fields such as physics, engineering, and computer science.
