Questions and Answers
For the given matrices $A = \begin{pmatrix} 1 & 5 \ 2 & 0 \ 3 & 4 \end{pmatrix}$ and $B = \begin{pmatrix} 1 & 3 \ 2 & 1 \end{pmatrix}$, what is the value of the element in the 2nd row and 1st column of the matrix $AB$?
4
If $X = \begin{pmatrix} 1 & 3 \ 2 & 4 \end{pmatrix}$ and $Y = \begin{pmatrix} 5 & 0 \ 1 & 2 \end{pmatrix}$, what is the value of the determinant of $XY - YX$?
0
If $A = \begin{pmatrix} 2 & 1 \ 3 & 4 \end{pmatrix}$ and $B = \begin{pmatrix} 5 & 4 \ 0 & 3 \end{pmatrix}$, what is the value of the determinant of $A^{-1}B$?
$\frac{23}{3}$
If $A = \begin{pmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{pmatrix}$ and $B = \begin{pmatrix} 9 & 8 & 7 \ 6 & 5 & 4 \ 3 & 2 & 1 \end{pmatrix}$, what is the value of the trace of $AB$?
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