Step 1: Read the matrix size
Count rows first, then columns. This matrix has 2 rows and 2 columns.
A = [1234]
size of A = 2 × 2
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Algebra
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Rows and columns
A matrix is a number grid
A is 2 × 2
A matrix stores numbers in rows and columns. The size is written as rows by columns.
Detailed notes
Worked Examples
Matrix operations are mostly size rules plus careful entry-by-entry arithmetic. Multiplication is the exception: it uses rows from the first matrix and columns from the second.
Step 2: Add matching entries
Addition only works when both matrices have the same size. Add each position to its matching position.
[1234] + [5678]
[1 + 52 + 63 + 74 + 8]
[681012]
Step 3: Subtract matching entries
Subtraction also needs the same size. Keep the order: first matrix minus second matrix.
[5678] - [1234]
[5 - 16 - 27 - 38 - 4]
[4444]
Step 4: Multiply rows by columns
Each answer entry comes from one row and one column. Write each product-sum on its own line so the row-column matches stay visible.
[1234] × [2012]
top left = 1×2 + 2×1 = 4
top right = 1×0 + 2×2 = 4
bottom left = 3×2 + 4×1 = 10
bottom right = 3×0 + 4×2 = 8
[44108]
Step 5: Divide by using an inverse
There is no direct matrix division. If B has an inverse, divide by B by multiplying by B inverse.
A ÷ B is not a direct operation
A ÷ B means A × B-1
AX = C, so X = A-1C
Step 6: Check whether the operation is allowed
Before calculating, check the sizes. This prevents most matrix mistakes.
add or subtract: 2 × 2 with 2 × 2
multiply: 2 × 3 with 3 × 2 gives 2 × 2
inverse: only square matrices can have B-1