That-Using properties of determinants- prove- 1 1-p 1-p-q- 2 3-2 p 4-3 p-2 q- 3 6-3 p 10-6 p-3 q -1

Expanding along C1, we have: Hence, the given result is proved. ...

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Invertible Element Binary Operation

that:Using pr...

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Using properties of determinants, prove that:

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∣ ∣ ∣ ∣ \begin{matrix} 1 & 1 + p & 1 + p + q 2 & 3 + 2 p & 4 + 3 p + 2 q 3 & 6 + 3 p & 10 + 6 p + 3 q \end{matrix} ∣ ∣ ∣ ∣

= 1

∣ ∣ ∣ ∣ \begin{matrix} 1 & 1 + p & 1 + p + q 2 & 3 + 2 p & 4 + 3 p + 2 q 3 & 6 + 3 p & 10 + 6 p + 3 q \end{matrix} ∣ ∣ ∣ ∣

Using properties of determinants prove the following questions.

$∣ ∣ ∣ ∣ \begin{matrix} 1 & 1 + p & 1 + p + q 2 & 3 + 2 p & 4 + 3 p + 2 q 3 & 6 + 3 p & 10 + 6 p + 3 q \end{matrix} ∣ ∣ ∣ ∣ = 1$

p

q

3 p + 4 q = - 1

6 p - 2 q = 8

\to p, \to q, \to r

\to p \times \to q = \to r

\to a

[\to a \to q \to r] = 1, [\to a \to r \to p] = 2

[\to a \to p \to q] = 3

\to a

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