If A=[−21−4−24−11−1−4] and B=[−242−4−11411] then AB=? BA=? True or false : AB=BA for any two square matrices A and B of the same size.

Question

If A=[−21−4−24−11−1−4] and B=[−242−4−11411]   then AB=?  BA=?  True or false : AB=BA for any two square matrices A and B of the same size.

svartmaleJ · Accepted Answer

Step 1  The given matrices are,  A=[−21−4−24−11−1−4] and B=[−242−4−11411]  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=[−21−4−24−11−1−4][−242−4−11411]  =[(−2⋅−2)+(1⋅−4)+(−4⋅4)(−2⋅4)+(1⋅−1)+(−4⋅1)(−2⋅2)+(1⋅1)+(−4⋅1)(−2⋅−2)+(4⋅−4)+(−1⋅4)(−2⋅4)+(4⋅−1)+(−1⋅1)(−2⋅2)+(4⋅1)+(−1⋅1)(1⋅−2)+(−1⋅−4)+(−4⋅4)(1⋅4)+(−1⋅−1)+(−4⋅1)(1⋅2)+(−1⋅1)+(−4⋅1)]  =[4−4+−16−8−1−4−4+1−44−16−4−8−4−1−4+4−1−2+4+−164+1−42−1−4]  =[−16−13−7−16−13−1−141−3]…(1)  Step 4  Similarly, evaluating BA  BA=[−242−4−11411][−21−4−24−11−1−4]  =[(−2⋅−2)+(4⋅−2)+(2⋅1)(−2⋅1)+(4⋅4)+(2⋅−1)(−2⋅−4)+(4⋅−1)+(2⋅−4)(−4⋅−2)+(−1⋅−2)+(1⋅1)(−4⋅1)+(−1⋅4)+(1⋅−1)(−4⋅−4)+(−1⋅−1)+(1⋅−4)(4⋅−2)+(1⋅−2)+(1⋅1)(4⋅1)+(1⋅4)+(1⋅−1)(4⋅−4)+(1⋅−1)+(1⋅−4)]

Jeffrey Jordon · Accepted Answer

Answer is given below (on video)

Jeffrey Jordon · Accepted Answer

Answer is given below (on video)

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.

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