Show that the determinant is equal to (x-y)(y-z)(z-x)

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The determinant of a matrix is a single numerical value which is used when calculating the inverse or when solving systems of linear equations.
The determinant of a matrix AA is denoted |A||A|, or sometimes det(A)det(A). The determinant is only defined for square matrices.
A matrix is said to be singular if its determinant is zero.
The general formula for the determinant of matrices of any size is very complicated. You will only be asked to compute the determinants of 2×22×2 or 3×33×3 matrices by hand.