Determine whether the statement are TRUE or FALSE. Write TRUE if the Statement is True and False otherwise. 19. The product of two m x n matrices is defined.20. For any matrices A and B, if the product AB is defined,then the product BA is also defined.21. For any matrices A and B, if the products AB and BA areboth defined, then AB = BA.22. If A is a square matrix, then A² is defined.23. If A and B are matrices, then both AB and BA are definedif and only if A and B are square matrices.24. If A is an m × n matrix and B is an n × p matrix, then(AB)" = A" B" .25. There exist nonzero matrices A and B for which AB = BA.26. For any matrices A and B for which the product AB isdefined, the jth column of AB equals the matrix-vectorproduct of A and the jth column of B.27. For any matrices A and B for which the product AB isdefined, the (i,j)-entry of AB equals aijbij.28. For any matrices A and B for which the product AB isdefined, the (i,j)-entry of AB equals the sum of the prod-ucts of corresponding entries from the ith column of Aand the jth row of B.29. If A, B, and C are matrices for which the product A(BC )is defined, then A(BC)= (AB)C. 30. If A and B are m x n matrices and C is an n x p matrix,then (A + B)C = AB +BC.31. If A and B are n x n matrices, then the diagonal entriesof the product matrix AB are a1¡b1,a22b22, . . . , anmbnn -32. If the product AB is defined and either A or B is a zeromatrix, then AB is a zero matrix.33. If the product AB is defined and AB is a zero matrix, theneither A or B is a zero matrix.34. If Aa and Ag are both 2 x 2 rotation matrices, then AqAßis a 2 x 2 rotation matrix.35. The product of two diagonal matrices is a diagonal matrix.

Note: There are multiple questions are given in one question. According to the rule, you will get…

19. The product of two m x n matrices is defined. 20. For any matrices A and B, if the product AB is defined, then the product BA is also defined. 21. For any matrices A and B, if the products AB and BA are both defined, then AB = BA. 22. If A is a square matrix, then A2² is defined. 23. If A and B are matrices, then both AB and BA are defined

19. The product of two m x n matrices is defined. 20. For any matrices A and B, if the product AB is defined, then the product BA is also defined. 21. For any matrices A and B, if the products AB and BA are both defined, then AB = BA. 22. If A is a square matrix, then A2² is defined. 23. If A and B are matrices, then both AB and BA are defined

C++ for Engineers and Scientists

4th Edition

ISBN:9781133187844

Author:Bronson, Gary J.

Publisher:Bronson, Gary J.

Chapter13: Structures

Section: Chapter Questions

Problem 4PP

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