Q2 of 29 Page 1

A and B are square matrices of order 3 each, |A| = 2 and |B| = 3. Find |3AB|.

We know that,


|AB| = |A||B|


⇒ |AB| = 2 × 3 = 6


When a matrix of order n is multiplied by a scalar“α”, the determinant of new matrix becomes “αn” times the determinant of original matrix


i.e. |αA| = αn|A|


⇒ |3AB| = 33|AB| = 27(6) = 162


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