Question:

Which one of the following is true always for any two non-singular matrices A and B of same order ?

Updated On: Jul 7, 2022
  • $AB = BA$
  • $(AB)^t = A^t B^t$
  • $(A+B)\,(A-B)=A^2-B^2$
  • $(AB)^{-1}=B^{-1}A^{-1}$
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The Correct Option is D

Solution and Explanation

Answer (d) $(AB)^{-1}=B^{-1}A^{-1}$
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Concepts Used:

Matrices

Matrix:

A matrix is a rectangular array of numbers, variables, symbols, or expressions that are defined for the operations like subtraction, addition, and multiplications. The size of a matrix is determined by the number of rows and columns in the matrix.

The basic operations that can be performed on matrices are:

  1. Addition of Matrices - The addition of matrices addition can only be possible if the number of rows and columns of both the matrices are the same.
  2. Subtraction of Matrices - Matrices subtraction is also possible only if the number of rows and columns of both the matrices are the same.
  3. Scalar Multiplication - The product of a matrix A with any number 'c' is obtained by multiplying every entry of the matrix A by c, is called scalar multiplication. 
  4. Multiplication of Matrices - Matrices multiplication is defined only if the number of columns in the first matrix and rows in the second matrix are equal. 
  5. Transpose of Matrices - Interchanging of rows and columns is known as the transpose of matrices.