Determinant of [6789]\left[\begin{array}{cc}6 & 7\\8 & 9\end{array}\right]

The calculator will find the determinant of the square 22x22 matrix [6789]\left[\begin{array}{cc}6 & 7\\8 & 9\end{array}\right], with steps shown.

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A

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Your Input

Calculate 6789\left|\begin{array}{cc}6 & 7\\8 & 9\end{array}\right|.

Solution

The determinant of a 2x2 matrix is abcd=adbc\left|\begin{array}{cc}a & b\\c & d\end{array}\right| = a d - b c.

6789=(6)(9)(7)(8)=2\left|\begin{array}{cc}6 & 7\\8 & 9\end{array}\right| = \left(6\right)\cdot \left(9\right) - \left(7\right)\cdot \left(8\right) = -2

Answer

6789=2\left|\begin{array}{cc}6 & 7\\8 & 9\end{array}\right| = -2A