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Properties of Determinants

If | A | = ...

Question

If $| A | = 2$ , where $A$ is a $3 \times 3$ matrix. Then find $| 3 A |$

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Solution

$| A | = 2$ ,
Scalar multiplication
$| 3 A | =$ 3*2=6

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A

is a matrix of order

3 \times 3

| a d j A |

| A | = 2

3 \times 3

matrix and |3A| = k |A|, then k =

A = [a_{i j}],

a_{i j} = (i + j)^{2}

B = - 3 A

B

.

A

3 \times 3

A^{T}

be transpose matrix of

A .

A = 3 A^{T} - 4 I,

I

is identity matrix of order

3,

det (A)

X

3 A - 2 B + 3 I + X = 0

A = [\begin{matrix} 4 & 2 1 & 3 \end{matrix}], B = [\begin{matrix} - 2 & 1 3 & 2 \end{matrix}]

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