Let A=begin{bmatrix}1 & 2 4 & -1 end{bmatrix} text{ and } B=begin{bmatrix}a & -3 -6& 1 end{bmatrix} . For what values of a (if any) do matrices A and B commute? None -2 -6 -1 -4

avissidep 2020-12-30 Answered
Let A=[1241] and B=[a361] . For what values of a (if any) do matrices A and B commute?
None
-2
-6
-1
-4
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Expert Answer

yunitsiL
Answered 2020-12-31 Author has 108 answers
Step 1
The given matrices are
A=[1241] and B=[a361]
The given two matrices A and B are said to be commutative if AB=BA.
Step 2
Solving AB=BA , we get
[1241][a361]=[a361][1241]
[a1214a+613]=[a122a+3213]
Now equating the elements ,
2a+3=1
a=2
and
4a+6=2
a=2
Step 3
Therefore, a=-2
Hence, option "2" is correct
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