Properties of Determinants | Mathematics

1. The value of a determinant is unaltered when the rows and columns are interchanged.
2. If any two rows or columns of a determinant are interchanged the value of the determinant is changed in its sign.
3. If any two rows or columns of a determinant are identical, then the value of the determinant is zero.
4. If each element of a row or column of a determinant is multiplied by any number K \neq 0, then the value of the determinant is multiplied by the same number K.
5. If each element of a row or column is expressed as the sum of two elements, then the determinant can be expressed as the sum of two determinants of the same order.
6. If each element of a row or column of a determinant is multiplied by a constant K \neq 0 and then added to or subtracted from the corresponding elements of any other row or column then the value of the determinant is unaltered.

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[abhipandey]

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[rakhiptk]

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[sonalichache]

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[hasininimasha]

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[mohith]

I confused little bit on last property and another all properities are well said ...thank you so much sir

[shiraz]

where do the d1 d2 and d3 derived from in the property 5

[haifa]

there is a big different between saying transport the matrix than saying interchange. go back and review your details corr3ectly

[shanmukh]

there is a big difference between transpose and inverse

[richardcao]

who else is here for their pre calc hw

[abhipandey]

Thank you apke jaisa you tube pe koi nahi... khaas baat ye hai ki aap typing bhi dete hai aur short time me poora explane kar dete hai ik baar fir se thank.... mujhe chemistry PG me bahut help mila ap se