Step by step
The question
Question: find the determinant of this matrix.
D = |−1, 5; 2, 3|
The determinant is one number we get from a square matrix.
We write the matrix between two straight lines, and call it D.
1 Multiply the diagonals
So D = −1 × 3 − 2 × 5.
D = −1 × 3 − 2 × 5
Careful!
Always down minus up.
Up minus down gives the wrong sign.
Careful: not 10 − (−3) ✗
2 Down minus up
−1 times 3 is −3.
2 times 5 is 10.
D = −3 − 10
−3 minus 10 is −13.
So D = −13.
D = −13
3 Check
Let's check the taking away by adding back: −13 + 10 = −3, the down product.
So D = −13 is right!
−13 + 10 = −3
Let's look back.
First: multiply the diagonals.
Then: down minus up.
Last: check.
Answer
D = −13