Question

q1. What is det ( k I) ?
(Order sqaure matrix I is 3)

q2. What is det ( A.adj A) of order 3 , if Det A is 3 ?

Answer 1

Before starting you must be knowing this,

1)det (I) = 1

2)det (kA) = $\sf{k^n} A$

where A is a matrix

where n is the order of the matrix

3)det (AB) = (detA)×(detB)

4)det(adjA) = $\sf{|A|^{n-1}}$

where n is the order of the matrix

Q1 - What is det ( k I) ?

(Order sqaure matrix I is 3

Ans : det(kI) = det(k)×det(I) = k³×1 = k³

Q2. What is det ( A.adj A) of order 3 , if Det A is 3 ?

Ans : det ( A.adj A) = det(A)×det(adj A)

= |A|× $\sf{|A|^{3-1}}$

= |A|× |A|² = |A|³

Answer 2

Before starting you must be knowing this,

1)det (I) = 1

2)det (kA) = $\sf{k^n} A$

where A is a matrix

where n is the order of the matrix

3)det (AB) = (detA)×(detB)

4)det(adjA) = $\sf{|A|^{n-1}}$

where n is the order of the matrix

Q1 - What is det ( k I) ?

(Order sqaure matrix I is 3

Ans : det(kI) = det(k)×det(I) = k³×1 = k³

Q2. What is det ( A.adj A) of order 3 , if Det A is 3 ?

Ans : det ( A.adj A) = det(A)×det(adj A)

= |A|× $\sf{|A|^{3-1}}$

= |A|× |A|² = |A|³