Precalculus : Solve a System of Equations Using the Multiplicative Inverse

Study concepts, example questions & explanations for Precalculus

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Example Questions

Example Question #2 : Inverses Of Matrices

What is the inverse of the identiy matrix  \(\displaystyle \begin{bmatrix} 1& 0\\ 0 &1 \end{bmatrix}\) ?

Possible Answers:

\(\displaystyle \begin{bmatrix} 2& -1\\-1 & 2 \end{bmatrix}\)

\(\displaystyle \begin{bmatrix} 1& 1\\ 1 & 1 \end{bmatrix}\)

\(\displaystyle \begin{bmatrix} 0&0 \\0 & 0 \end{bmatrix}\)

The identity matrix \(\displaystyle \begin{bmatrix} 1&0 \\0 & 1 \end{bmatrix}\)

Correct answer:

The identity matrix \(\displaystyle \begin{bmatrix} 1&0 \\0 & 1 \end{bmatrix}\)

Explanation:

By definition, an inverse matrix is the matrix B that you would need to multiply matrix A by to get the identity. Since the identity matrix yields whatever matrix it is being multiplied by, the answer is the identity itself.

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