Let and . Consider the products and . Which statement is…

MATHEMATICS · Single correct · AP · AP Precalculus · Functions with Parameters, Vectors, and Matrices · Functions with Parameters, Vectors, and Matrices

Problem

Let

M=\begin{pmatrix}1&2&0\\0&1&0\\0&0&1\end{pmatrix}

and

N=\begin{pmatrix}1&-2&0\\0&1&0\\0&0&1\end{pmatrix}

. Consider the products

MN

and

NM

. Which statement is correct? (a)

MN=I_3

but

NM\ne I_3

(b)

MN=M

and

NM=N

MN

and

NM

are equal to

I_3

(d)

NM=I_3

but

MN\ne I_3

Related theory

Matrix Operations
Matrices
Multiplication of matrices

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