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Inverse Matrix (Theorems)

Video Lecture Theorem I : The inverse of a square matrix, if it exists, is unique. Proof : Let A be a square matrix of order n such that inverse of A exists. Let B and C be any two inverse of A . Any two inverse of A are equal matrices. The inverse of A is unique. Theorem II : A square matrix is invertible if and only if it is non-singular. Proof : Let the square matrix A be invertible. There exists a square matrix B such that AB = BA = I . The number | A| is non-zero, for otherwise | A|.|B| will become zero. The matrix A is non-singular. Theorem III : If A and B are invertible matrices of order n , then show that AB is also invertible and . Proof : The matrice...

Adjoint of a Matrix

Video Lecture The Adjoint of a square matrix is defined as the transpose of the matrix , where is the co-factor of the element . Adjoint of the matrix A is denoted by Let then

Elementary Operation of a Matrix

Video Lecture There are generally three types of Elementary Operation of a Matrix : (1) Interchange of any two rows or column. e.g. : Let, interchange in a matrix A, we get after interchanging other rows are not affected by them. Similarly, ...

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