Question

Let A = $\begin{bmatrix}

• 1 & 2 & - 3 \
• 2 & 0 & 3 \ 3 & - 3 & 1 \end{bmatrix}$be a matrix, then

(determinant of A ) × (adjoint of inverse of A) is equal to-

• A. O_{3 × 3}
• B. $\begin{bmatrix}
  • 1 & 2 & - 3 \
  • 2 & 0 & 3 \ 3 & - 3 & 1 \end{bmatrix}$
• C. I₃
• D. $\begin{bmatrix}
  • 3 & - 3 & 1 \ 3 & 0 & - 2 \
  • 1 & 2 & - 3 \end{bmatrix}$

Answer 1

Answer: (B)

$\begin{bmatrix}

• 1 & 2 & - 3 \
• 2 & 0 & 3 \ 3 & - 3 & 1 \end{bmatrix}$

Answer 2

|A| adj (A^–1) = ?

A^–1 adj (A^–1) = |A^–1| I₃

Ž A. A^–1 adj (A^–1) = |A^–1| AI₃

Ž adj (A^–1) = |A^–1| A

Ž |A| adj (A^–1) = A

Here |A| = 13 But |A| ¹ 0