Q&A - Ask Doubts and Get Answers
Q

Let A be a nonsingular square matrix of order 3 × 3. Then |adj A| is equal to (A) | A | (B) | A |^2 (C) | A |^3 (D)3| A |

Q : 17        Let A be a nonsingular square matrix of order \small 3\times 3. Then \small |adjA| is equal to

                 (A) \small |A|      (B) \small |A|^2      (C) \small |A|^3      (D) \small 3|A|

Answers (1)
Views

We know the identity (adjA)A = |A| I

Hence we can determine the value of |(adjA)|.

Taking both sides determinant value we get,

|(adjA)A| = ||A| I|     or   |(adjA)||A| = ||A||| I|

or taking R.H.S.,

||A||| I| = \begin{vmatrix} |A| & 0&0 \\ 0&|A| &0 \\ 0&0 &|A| \end{vmatrix}

= |A| (|A|^2) = |A|^3

or, we have then |(adjA)||A| = |A|^3    

Therefore |(adjA)| = |A|^2

Hence the correct answer is B.

 

Exams
Articles
Questions