Question
Download Solution PDFConsider the following in respect of the matrix
1. Inverse of A does not exist
2. A3 = A
3. 3A = A2
Which of the above are correct?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
Matrix Multiplication:
- Two matrices can only be multiplied when the column number of the first matrix is equal to the row number of the second matrix
- If A is not an invertible matrix then |A| = 0
- If A is a singular matrix then |A| = 0
Calculation:
Given that,
⇒ |A| = 1(1 - 1) - 1(1 - 1) + 1 (1 - 1) = 0
Hence, Inverse of A does not exist.
⇒ A2 =
⇒ A2 =
⇒ A3 = A2 . A
⇒ A3 =
⇒ A3 =
⇒ A3 = 9
Hence, statement (2) is incorrect.
Now, the value of 3A is
= 3
⇒ 3A =
∴ 3A = A2
Hence, statement (3) is correct.
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