Question
Download Solution PDFComprehension
Direction: Consider the following for the next 02 (two) items:
Let A and B be (3 × 3) matrices with det A = 4 and det B = 3
What is det (3AB-1) equal to?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
If A and B are square matrices of order n, then det (m × AB) = mn × det (A) × det (B) where m ∈ R is a scalar.
If A is a non – singular square matrix of order n, then det (A-1) = 1/det (A)
Calculation:
Given: Given: A and B be (3 × 3) matrices with det A = 4 and det B = 3
As we know that, if A and B are square matrices of order n, then det (m × AB) = mn × det (A) × det (B) where m ∈ R is a scalar.
⇒ det (3AB-1) = 33 × det (A) × det (B- 1)
As we know that, If A is a non – singular square matrix of order n, then det (A-1) = 1/det (A)
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