Question

If ais a square matrix of order 3 such that |adja|=25 find|a|

Answer 1

Answer:

|A|=5.

The solution is given in the above attachment.

Answer 2

Answer:

If |adj(a)| = 25, then the determinant of the matrix 'a' is either +5 or -5.

Step-by-step explanation:

From the above question,

They have given :

The determinant of a square matrix 'a' is denoted by '|a|'. The adjugate of a square matrix 'a' is denoted by 'adj(a)'. The relationship between the determinant of a matrix and its adj gate is given by:

A square matrix of order 3 is a matrix that has 3 rows and 3 columns. It is a square-shaped matrix and has 3 elements in each row and column. The determinant of a 3x3 matrix can be calculated using the following formula:

|a| = a11 * (a22 * a33 - a23 * a32) - a12 * (a21 * a33 - a23 * a31) + a13 * (a21 * a32 - a22 * a31)

where aij represents the element in the ith row and jth column of the matrix.

| a | * | adj(a) | = | a | * | a | = | a |$.^{2}$

So, if |adj(a)| = 25,

     then |a|$.^{2}$ = 25, and

               |a| = ± sqrt(25) = ± 5.

Therefore, if |adj(a)| = 25, then the determinant of the matrix 'a' is either +5 or -5.

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