Product Of Tow Determinants Assignment Help | Product Of Tow Determinants Homework Help

Product of Tow Determinants

Theorem. The determinant of the product of two matrices of order n is the product of their determinants. That is, |AB| = |A| |B|.

Example. Let


|AB| = |A| . |B| =   = (3) (3) = 9.

Remark. Since we known that for any square matrix A, |A| = |A’|, we have |AB| = |A| |B| = |A’| |B’| =  |A| |B’|. Thus, the product of two determinants can be written in terms of row by column as in matrices or unlike matrices column by column, column by row or row by row.

Example. Show that

Hence evaluate the determinant on the right.

Solution. Let


Δ2 = 4a2 b2 c2

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