Consider the following statements:1. If A′ = A; then A is a singula

1.	Consider the following statements:1. If A′ = A; then A is a singular matrix, where A′ is the transpose of A.2. If A is a square matrix such that A3 = I, then A is non-singular.Which of the statements given above is/are correct ?1. 1 only 2. 2 only 3. Both 1 and 24. Neither 1 nor 2
Answer» Correct Answer - Option 2 : 2 only Concept: A matrix is singular if and only if its determinant is zero. Calculation: If A′ = A; where A′ is the transpose of A then \|A\| = \|A'\| But it is not necessary that \|A\| = 0, so A is not a singular matrix. Hence, Statement 1 is wrong. Given, A3 = I Taking determinants both sides, we get ⇒\|A3 \| = \|I\| = 1 ⇒ \|A\| = 1 Here, \|A\|≠ 0 so, A is a non-singular matrix Hence, option (2) is correct.

Consider the following statements:1. If A′ = A; then A is a singular matrix, where A′ is the transpose of A.2. If A is a square matrix such that A3 = I, then A is non-singular.Which of the statements given above is/are correct ?1. 1 only 2. 2 only 3. Both 1 and 24. Neither 1 nor 2

Answer» Correct Answer - Option 2 : 2 only

Concept:

A matrix is singular if and only if its determinant is zero.

Calculation:

If A′ = A; where A′ is the transpose of A then |A| = |A'|

But it is not necessary that |A| = 0, so A is not a singular matrix.

Hence, Statement 1 is wrong.

Given, A3 = I

Taking determinants both sides, we get

⇒|A3 | = |I| = 1

⇒ |A| = 1

Here, |A|≠ 0 so, A is a non-singular matrix

Hence, option (2) is correct.

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