Question

question 36 points 1

when matrix a and its inverse matrix \\(a^{-1}\\) are multiplied then the result is an ---------- matrix.

identity

inverse

Explanation:

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<reasoning>

Define matrix multiplication with its inverse

Using the Matrix Inverse Formula and Matrix Terminology knowledge points
\[
A \cdot A^{-1} = A^{-1} \cdot A = I
\]

Identify the resulting matrix type

Using the Matrix Terminology knowledge point
\[
I = \text{identity matrix}
\]
</reasoning>

<answer>
<mcq-correct>identity</mcq-correct>
<mcq-option>inverse</mcq-option>
</answer>

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"Mathematics",
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Answer:

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</pre_analysis>

<reasoning>

Define matrix multiplication with its inverse

Using the Matrix Inverse Formula and Matrix Terminology knowledge points
\[
A \cdot A^{-1} = A^{-1} \cdot A = I
\]

Identify the resulting matrix type

Using the Matrix Terminology knowledge point
\[
I = \text{identity matrix}
\]
</reasoning>

<answer>
<mcq-correct>identity</mcq-correct>
<mcq-option>inverse</mcq-option>
</answer>

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"Mathematics",
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"Matrix Terminology"
]
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