CCSS.Math.Content.HSN-VM.C.10
The Standard
(+) Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers. The determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse.
Common Core State Standards for Mathematics · Vector and Matrix Quantities
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students use zero matrices in addition and identity matrices in multiplication, choosing dimensions that make each operation valid. They calculate determinants and use the result to decide whether an inverse exists.
What Mastery Looks Like
- Students choose zero and identity matrices with the correct dimensions and predict their effect in an operation. They use the determinant to decide whether a square matrix has an inverse.
Common Misconceptions
- Students may treat the zero matrix and identity matrix as interchangeable. They may use an identity matrix of the wrong size or think a zero determinant means the inverse is the zero matrix.
How to Assess It
- Give A = [[2, 1], [3, 2]]. Ask students to find A + 0, AI, det(A), and state whether A has an inverse.
Lesson moves
Ways to Teach It
Give students matrix cards and operation cards, then have them match each matrix with the correct zero or identity matrix.
Ask students to explain why multiplying by an identity matrix leaves a matrix unchanged, using one numerical example.
Play a sorting game where students classify square matrices as invertible or not invertible after calculating each determinant.
Encode coordinate pairs with an invertible matrix, then discuss why decoding fails when the chosen matrix has determinant zero.
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Printable HSN-VM.C.10 Worksheet
A ready-to-print activity worksheet aligned to CCSS.Math.Content.HSN-VM.C.10, with an answer key for the teacher on its own page. No account needed.
PDF, US Letter, prints cleanly in black and white.
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Where This Standard Sits
Before This Standard
If students are struggling here, check these first.
- CCSS.Math.Content.HSN-VM.C.8
Knowing how matrix addition and multiplication work is necessary to understand zero matrices, identity matrices, and what a matrix inverse means.
- CCSS.Math.Content.HSN-VM.C.9
Matrix multiplication properties prepare students to understand identity matrices and why inverses must work under matrix multiplication rules.
What This Unlocks
Mastery here sets students up for these next.
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