# 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

Let . For what values of a (if any) do matrices A and B commute?
None
-2
-6
-1
-4
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yunitsiL
Step 1
The given matrices are

The given two matrices A and B are said to be commutative if AB=BA.
Step 2
Solving AB=BA , we get
$\left[\begin{array}{cc}1& 2\\ 4& -1\end{array}\right]\left[\begin{array}{cc}a& -3\\ -6& 1\end{array}\right]=\left[\begin{array}{cc}a& -3\\ -6& 1\end{array}\right]\left[\begin{array}{cc}1& 2\\ 4& -1\end{array}\right]$
$\left[\begin{array}{cc}a-12& -1\\ 4a+6& -13\end{array}\right]=\left[\begin{array}{cc}a-12& 2a+3\\ -2& -13\end{array}\right]$
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