Algebra — AQA GCSE Further Mathematics
Teaching note based on the AQA specification.
Test yourself on Algebra with AQA GCSE practice questions.
A week of Premium from your first lesson · Then the free plan continues · No card, no charge
Algebra explained
This statement asks you to know the identity matrix for a 2 × 2 matrix only, so you should not extend it to 3 × 3 or other sizes in the assessment.
Read the full explanation
The 2 × 2 identity matrix I has ones on the leading diagonal and zeros elsewhere: I = [[1, 0], [0, 1]]. Its key property is that it leaves any 2 × 2 matrix unchanged when multiplied, so I × A = A and A × I = A. For example, [[1, 0], [0, 1]] × [[2, 1], [0, 3]] gives [[2, 1], [0, 3]], because each entry of the product is a row of I multiplied by a column of A. Recognising I helps you simplify expressions and check working quickly.
Your focus
- Write the 2 × 2 identity matrix from memory.
- Show by calculation that I × A = A for a given 2 × 2 matrix A.
- Identify the identity matrix in a 2 × 2 product and simplify the product accordingly.
Algebra exam tips
Marking Points
- States I as [[1, 0], [0, 1]], with ones on the leading diagonal and zeros elsewhere.
- Keeps the matrix to two rows and two columns, matching the 2 × 2 scope.
- Shows that I × A = A and A × I = A for a given 2 × 2 matrix A.
- Multiplies row by column correctly for each entry when checking a product with I.
- Distinguishes the identity matrix from the number 1 by its matrix form.
Examiner Tips
- 💡Write out the 2 × 2 grid with four entries before filling it in, so the diagonal positions are clear.
- 💡Check a product by confirming that the result equals the original matrix A when I is multiplied on either side.
- 💡Use the 2 × 2 form only when the question specifies a 2 × 2 matrix, and state its size in your working.
Common Mistakes
- Writes the 3 × 3 identity matrix when the question asks for the 2 × 2 case; keep to two rows and two columns.
- Places 1s off the leading diagonal, such as [[0, 1], [1, 0]], which is a different matrix; keep the 1s from top left to bottom right.
- Multiplies entries position by position instead of row by column; use the row-by-column rule for every entry of the product.
- Treats I as a matrix of all ones; keep zeros in the off-diagonal positions.