MA19.A2.5

Mathematics (2019) Grade(s): 09-12 - Algebra II with Statistics

MA19.A2.5
Describe the roles that zero and identity matrices play in matrix addition and multiplication, recognizing that they are similar to the roles of 0 and 1 in the real numbers.

Unpacked Content

Knowledge

Students know:

The additive and multiplicative identity properties for real numbers.
The aspects of the zero and identity matrices.
A matrix multiplied by its multiplicative inverse equals the identity matrix.

Skills

Students are able to:

Find the determinant of a square matrix.
Find the multiplicative inverse of a square matrix.
Add and multiply matrices.

Understanding

Students understand that:

Identity properties that apply to other number systems apply to matrices.
The multiplicative inverse property that applies to other number systems applies to matrices.
A matrix with a determinant equal to zero does not have a multiplicative inverse analogous to zero in the real number system not having a multiplicative inverse.
Division by zero in the real number system is undefined.

Vocabulary

Zero Matrix
Identity Matrix
Determinant
Multiplicative Inverse

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