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If A and B and C are 4x4 random square matrices, which of the following are always true? (more than one answer may be correct). a.A*(B*C) = (A*B)*(A*C)   b.transpose(A * B) = transpose(A) * transpose(B)   c.(A + B) + C ≠ A + (B + C)   d.A*(B + C) = A*B + A*C   e.transpose(A * B) = transpose(B) * transpose(A)   f.If A is an identity matrix, then A*B=B*A   Multiple-choice questions

If A and B and C are 4x4 random square matrices, which of the following are always true? (more than one answer may be correct). a.A*(B*C) = (A*B)*(A*C)   b.transpose(A * B) = transpose(A) * transpose(B)   c.(A + B) + C ≠ A + (B + C)   d.A*(B + C) = A*B + A*C   e.transpose(A * B) = transpose(B) * transpose(A)   f.If A is an identity matrix, then A*B=B*A   Multiple-choice questions

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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If A and B and C are 4x4 random square matrices, which of the following are always true? (more than one answer may be correct).

a.A*(B*C) = (A*B)*(A*C)
 
b.transpose(A * B) = transpose(A) * transpose(B)
 
c.(A + B) + C ≠ A + (B + C)
 
d.A*(B + C) = A*B + A*C
 
e.transpose(A * B) = transpose(B) * transpose(A)
 
f.If A is an identity matrix, then A*B=B*A
 
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