If A=begin{bmatrix}-2 & 1&-4 -2 & 4&-1 1 &-1 &-4 end{bmatrix} text{ and } B=begin{bmatrix}-2 & 4&2 -4 & -1&1 4 &1 &1 end{bmatrix} then AB=? BA=? True or false : AB=BA for any two square matrices A and B of the same size.

Ava-May Nelson 2020-11-10 Answered
If A=[214241114] and B=[242411411]
then AB=?
BA=?
True or false : AB=BA for any two square matrices A and B of the same size.
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Expert Answer

svartmaleJ
Answered 2020-11-11 Author has 92 answers
Step 1
The given matrices are,
A=[214241114] and B=[242411411]
Step 2
To find the value of AB, BA and telling whether AB=BA is true or not for any two square matrices of the same size.
Step 3
Taking the product of matrices, and evaluating AB,
AB=[214241114][242411411]
=[(22)+(14)+(44)(24)+(11)+(41)(22)+(11)+(41)(22)+(44)+(14)(24)+(41)+(11)(22)+(41)+(11)(12)+(14)+(44)(14)+(11)+(41)(12)+(11)+(41)]
=[44+168144+1441648414+412+4+164+14214]
=[16137161311413](1)
Step 4
Similarly, evaluating BA
BA=[242411411][214241114]
=[(22)+(42)+(21)(21)+(44)+(21)(24)+(41)+(24)(42)+(12)+(11)(41)+(14)+(11)(44)+(11)+(14)(42)+(12)+(11)(41)+(14)+(11)(44)+(11)+(14)]
Jeffrey Jordon
Answered 2022-01-23 Author has 2262 answers

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