Determinant of [2356]\left[\begin{array}{cc}2 & 3\\5 & 6\end{array}\right]

The calculator will find the determinant of the square 22x22 matrix [2356]\left[\begin{array}{cc}2 & 3\\5 & 6\end{array}\right], with steps shown.

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A

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Your Input

Calculate 2356\left|\begin{array}{cc}2 & 3\\5 & 6\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.

2356=(2)(6)(3)(5)=3\left|\begin{array}{cc}2 & 3\\5 & 6\end{array}\right| = \left(2\right)\cdot \left(6\right) - \left(3\right)\cdot \left(5\right) = -3

Answer

2356=3\left|\begin{array}{cc}2 & 3\\5 & 6\end{array}\right| = -3A