Q. 145.0( 2 Votes )

If and , then verify (BA)2 ≠ B2A2.

Answer :

We have,



We need to verify (BA)2 ≠ B2A2.


Take L.H.S: (BA)2


First, compute BA.



We know what order of matrix is,


If a matrix has M rows and N columns, the order of matrix is M × N.


Order of matrix B:


Number of rows = 2


M = 2


Number of columns = 3


N = 3


Then, order of matrix = M × N


Order of matrix B = 2 × 3


Order of matrix A:


Number of rows = 3


M = 3


Number of columns = 2


N = 2


Then, order of matrix = M × N


Order of matrix A = 3 × 2


Since, in order to multiply two matrices, A and B, the number of columns in A must equal the number of rows in B. Thus, if A is an m x n matrix and B is an r x s matrix, n = r.


So, A and B can be multiplied.



Multiply 1st row of matrix B by matching member of 1st column of matrix A, then sum them up.


(2, 1, 2)(3, 1, 2) = (2 × 3) + (1 × 1) + (2 × 2)


(2, 1, 2)(3, 1, 2) = 6 + 1 + 4


(2, 1, 2)(3, 1, 2) = 11



Multiply 1st row of matrix B by matching member of 2nd column of matrix A, then sum them up.


(2, 1, 2)(-4, 1, 0) = (2 × -4) + (1 × 1) + (2 × 0)


(2, 1, 2)(-4, 1, 0) = -8 + 1 + 0


(2, 1, 2)(-4, 1, 0) = -7



Multiply 2nd row of matrix B by matching member of 1st column of matrix A, then sum them up.


(1, 2, 4)(3, 1, 2) = (1 × 3) + (2 × 1) + (4 × 2)


(1, 2, 4)(3, 1, 2) = 3 + 2 + 8


(1, 2, 4)(3, 1, 2) = 13



Multiply 2nd row of matrix B by matching member of 2nd column of matrix A, then sum them up.


(1, 2, 4)(-4, 1, 0) = (1 × -4) + (2 × 1) + (4 × 0)


(1, 2, 4)(-4, 1, 0) = -4 + 2 + 0


(1, 2, 4)(-4, 1, 0) = -2



So,


(BA)2 = (BA).(BA)



Similarly,





Take R.H.S: B2A2


Let us first compute B2.


B2 = B.B



In order to multiply two matrices, A and B, the number of columns in A must equal the number of rows in B. Thus, if A is an m x n matrix and B is an r x s matrix, n = r.


Note that in matrix B, number of columns ≠ number of rows.


This means, we can’t find B2.


L.H.S ≠ R.H.S


Thus, (BA)2 ≠ B2A2.


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Triangular Matrices & operations on matricesTriangular Matrices & operations on matricesTriangular Matrices & operations on matrices58 mins
Determinants of Matrices of different orderDeterminants of Matrices of different orderDeterminants of Matrices of different order59 mins
Types of Matrices & PropertiesTypes of Matrices & PropertiesTypes of Matrices & Properties51 mins
Determining a determinantDetermining a determinantDetermining a determinant63 mins
Lecture on Product of DeterminantsLecture on Product of DeterminantsLecture on Product of Determinants58 mins
Know About finding the Adjoint & Inverse Of MatrixKnow About finding the Adjoint & Inverse Of MatrixKnow About finding the Adjoint & Inverse Of Matrix46 mins
Test Yourself, Properties of DeterminantsTest Yourself, Properties of DeterminantsTest Yourself, Properties of Determinants30 mins
Interactive Quiz on Matrices & DeterminantsInteractive Quiz on Matrices & DeterminantsInteractive Quiz on Matrices & Determinants48 mins
Interactive Quiz on Properties of DeterminantsInteractive Quiz on Properties of DeterminantsInteractive Quiz on Properties of Determinants43 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses