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A matrix A of order 3×3 has determinant 22 .What is the value of |4A| ?

as per the property of determinants,
if each element of a row (or a column) of a determinant is multiplied by a constant k, then its determinant value gets multiplied by k.
i.e., |kA| = k|A|

=> |A| = 22                  ..... (given)
=>|4A| = 4|A| = 4x22 = 88

=> |4A|  = 88 
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as per the property of determinants,
if each element of a row (or a column) of a determinant is multiplied by a constant k, then its determinant value gets multiplied by k.
i.e., |kA| = k|A|

=> |A| = 22                  ..... (given)
=>|4A| = 4|A| = 4x22 = 88

=> |4A|  = 88 
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|kA| = k|A|

= |A| = 22                  ..... (given)
= |4A| = 4^3|A|
= 64×22
= 1408
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let m be any constant and A be any matrix of order 3×3.

now ,when we write m×A it means that m is multiplied with each element which means:-
|m×A| = m^3|A|
as we can take m common from each row/column.

Therefore, if |A|=22
then, |4A| = 4^3|A|
=> 64×22 = 1408
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