**GCSE** **Mathematics**** Question Analysis Topic: Mathematics - Matrices**

**Exam Questions:**

1) If A is a 3×3 matrix such that |A|=8, then |3A| equals:

A) 8

B) 24

C) 72

D) 216

2) If A is a skew symmetric matrix of order 3, then the value of |A| is

A) 3

B) 0

C) 9

D) 27

**Answer:**

For GCSE Mathematics, you should know:

1) Since we are given |A| = 8,

we can deduce that |kA| = k^{n}|A| (n is A's order)

As such, |3A| = 3^{3}|A| = 3^{3 }x 8 = 27 x 8 (as A is a 3 by 3 matrix)

= 216. Hence, (D) is the right answer.

2) A is a skew symmetric matrix, i.e. A^{T} = -A

==> | - A | = (-1)^{n}|A|, where n is the order.

Substituing 3 in, we get -|A|.

Substituting into (i),

|A^{T}| = -|A|

==> -|A| = |A^{T}| (ii)

For any matrix,

|A| = |A^{T}|

Replacing these into (ii),

|A| = -|A|

==> 2|A| = 0

==> |A| = 0

Work hard for your GCSE Mathematics examination!

End of analysis. Great!