Question

if a is orthogonal matrix of order 3 then det(adj2A) is​

Answer 1

Answer:

64

Step-by-step explanation:

For any orthogonal matrix ;

| A | = +- 1

Det ( adj 2A) = { 2^n x |A| }^n-1

Here A is the matrix and n is the dimensions of the orthogonal matrix

In the given case, n = 3

Putting the values;

Det ( adj 2A) = { 2^3 x |+-1| }^3-1

Det ( adj 2A) = { 8 x |+-1| }^2

Det ( adj 2A) = 64

Answer 2

det(adj2A) = 64

Step-by-step explanation:

The determinant of an orthogonal matrix is always ± 1.

⇒ |A| = ±1

The order of the matrix is 3 × 3.

The formula is given as:

det(adj2A) = (2ⁿ. |A|)ⁿ⁻¹

Where,

n = Order of matrix = 3

Now,

det(adj2A) = (2³. |A|)³⁻¹

det(adj2A) = (2³. |A|)²

det(adj2A) = (2³)² (±1)²

det(adj2A) = (2)⁶ (1)

∴ det(adj2A) = 64