Q. 334.0( 3 Votes )

If A and B are sq

Answer :

We are given that,

A and B are square matrices of order 3.


|A| = -1, |B| = 3


We need to find the value of |3AB|.


By property of determinant,


|KA| = Kn|A|


If A is of nth order.


If order of A = 3 × 3


And order of B = 3 × 3


Order of AB = 3 × 3 [, Number of columns in A = Number of rows in B]


We can write,


|3AB| = 33|AB| [, Order of AB = 3 × 3]


Now, |AB| = |A||B|.


|3AB| = 27|A||B|


Putting |A| = -1 and |B| = 3, we get


|3AB| = 27 × -1 × 3


|3AB| = -81


Thus, the value of |3AB| = -81.


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