A = [(1,-3,1)(2,0,4)(1,2,-2)] 1. Calculate |A| 2. Find |adjA| {Hint: using the property A × adjA = |A|I} 3. Find |3A|

Question

A = \(\begin{bmatrix} 1 & -3 & 1 \\ 2 & 0 & 4 \\ 1 & 2 & -2 \end{bmatrix} \)

1. Calculate |A| 

2. Find |adjA| {Hint: using the property A × adjA = |A|I}

3. Find |3A|

Answer 1

1. |A| = \(\begin{bmatrix} 1 & -3 & 1 \\ 2 & 0 & 4 \\ 1 & 2 & -2 \end{bmatrix} \) = -28

2.  A x adj A = |A|I

3. |3A| = 27 × |A| = 27 × -28 = -756.