Chapter 10: Q83. (page 530)

Find the inverse of the matrix
$[\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}]$
if it exists.

Short Answer

Expert verified

The inverse of the given matrix is

[\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}]

Step by step solution

Step 1. Write down the given equation.

The given matrix is say

P = [\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}]

Step 2. Concept used.

The inverse of the matrix $A = [\begin{matrix} a & b \\ c & d \end{matrix}]$

exits if $|A| \neq 0$ . And inverse of

A = [\begin{matrix} a & b \\ c & d \end{matrix}]

is given by the formula:

A^{- 1} = \frac{1}{|A|} [\begin{matrix} d & - b \\ - c & a \end{matrix}]

where $|A| \neq 0$ .

Step 3. Evaluating inverse of given matrix.

The inverse of the matrix is evaluated as:

$\begin{array}{l} P = [\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}] .... (Given) \\ |P| = 1 - 0 \\ = 1 \end{array}$

Now evaluating inverse of role="math" localid="1648234505353" $P = [\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}]$

by the formula stated above.

$\begin{array}{l} P^{- 1} = \frac{1}{|1|} [\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}] \\ = [\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}] \end{array}$

Step 4. Conclusion.

Hence the inverse of the given matrix is $[\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}]$ .

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Find the inverse of the matrix
$[\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}]$
if it exists.

Short Answer

Step by step solution

Step 1. Write down the given equation.

Step 2. Concept used.

Step 3. Evaluating inverse of given matrix.

Step 4. Conclusion.

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Find the inverse of the matrix 1001if it exists.

Short Answer

Step by step solution

Step 1. Write down the given equation.

Step 2. Concept used.

Step 3. Evaluating inverse of given matrix.

Step 4. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

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Study anywhere. Anytime. Across all devices.

Find the inverse of the matrix
$[\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}]$
if it exists.