Q. 23.8( 17 Votes )

# If A is a 3 × 3 matrix such that |A| ≠ 0 and |3A| = k|A| then write the value of k.

Answer :

Theorem: If Let A be k × k matrix then |pA|=p^{k}|A|.

Given: k=3 and p=3.

|3A|=3^{3} × |A|

=27|A|.

Comparing above with k|A| gives k=27.

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