Question:
Let A and B be two non zero square matrices and AB and BA both are defined. It means
Let A and B be two non zero square matrices and AB and BA both are defined. It means
Updated On: May 22, 2025
- No. of columns of A # No. of rows of B
- No. of rows of A # No. of columns of B
- Both matrices (A) and (B) have same order
- Both matrices (A) and (B) does not have same order
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The Correct Option is C
Solution and Explanation
Given two non-zero square matrices, A and B
The definition of Matrix AB is Columns equal to B's Rows.
And BA is defined as follows: B's columns equal A's rows.
Therefore, it is correct that matrices (A) and (B) have the same order.
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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:
- 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.
- Subtraction of Matrices - Matrices subtraction is also possible only if the number of rows and columns of both the matrices are the same.
- 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.
- 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.
- Transpose of Matrices - Interchanging of rows and columns is known as the transpose of matrices.