Which of the following statements is false:

Question

Which of the following statements is false: (A) If |A|=0, then operatornameladj A mid=0 (B) Adjoint of a diagonal matrix of order 3 × 3 is a diagonal matrix (C) Product of two upper triangular matrices is a upper triangular matrix (D)  operatornameadj(A B)= operatornameadj(A) operatornameadj(B)

Tardigrade Admin · Accepted Answer

We have operatornameadj(A B)= operatornameadj(B) operatornameadj(A) text and not operatornameadj(A B)= operatornameadj(A) operatornameadj(B)

Q. Which of the following statements is false:

If $∣ A ∣ = 0$ , then $ladj A ∣= 0$

Adjoint of a diagonal matrix of order $3 \times 3$ is a diagonal matrix

Product of two upper triangular matrices is a upper triangular matrix

$adj (A B) = adj (A) adj (B)$

We have
$adj (A B) = adj (B) adj (A)$
$and not adj (A B) = adj (A) adj (B)$

Q. Which of the following statements is false:

If ∣A∣=0, then ladjA∣=0

Adjoint of a diagonal matrix of order 3×3 is a diagonal matrix

Product of two upper triangular matrices is a upper triangular matrix

adj(AB)=adj(A)adj(B)

We have adj(AB)=adj(B)adj(A) and not adj(AB)=adj(A)adj(B)

If $∣ A ∣ = 0$ , then $ladj A ∣= 0$

Adjoint of a diagonal matrix of order $3 \times 3$ is a diagonal matrix

$adj (A B) = adj (A) adj (B)$

We have
$adj (A B) = adj (B) adj (A)$
$and not adj (A B) = adj (A) adj (B)$