Question

If a is a square matrix of order 3, with |a|=9,then write the value of |2.Adja|

Answer 1

Answer with explanation:

It is given that ,a is square matrix of order 3, means there are 3 rows and 3 columns in that matrix.

|a|=9,

→Determinant A=9

→|2 × Adj.a |

=2³×|Adj.a |→a is a square matrix of order 3

→$a^{-1}$=Adj.a ×|a|

Taking "determinant" on both sides

→|$a^{-1}$|=||Adj.a|×|a||

Determinant of inverse of a=|a|

→|a|=|Adj.a|×|a|

→|Adj.a|=1--------------(1)

⇒|2 × Adj.a | =2³×|Adj.a |

=8×1=8-----[using 1]

Answer 2

|A|=9, Order of the matrix=3

Now,

=|2.adjA|

= 2^3|adjA|

=8|adjA|

=8x|A|^3-1

=8x|A|^2

=8x9^2

=8x81

=648