Determinant of [1245]\left[\begin{array}{cc}1 & 2\\4 & 5\end{array}\right]

The calculator will find the determinant of the square 22x22 matrix [1245]\left[\begin{array}{cc}1 & 2\\4 & 5\end{array}\right], with steps shown.

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A

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Your Input

Calculate 1245\left|\begin{array}{cc}1 & 2\\4 & 5\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.

1245=(1)(5)(2)(4)=3\left|\begin{array}{cc}1 & 2\\4 & 5\end{array}\right| = \left(1\right)\cdot \left(5\right) - \left(2\right)\cdot \left(4\right) = -3

Answer

1245=3\left|\begin{array}{cc}1 & 2\\4 & 5\end{array}\right| = -3A