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The determinant of matrix A is 5 and the determinant of matrix B is 40. The determinant of matrix AB is?
By BYJU'S Exam Prep
Updated on: September 25th, 2023
The determinant of matrix AB is 200 when the determinant of matrix A is 5 and the determinant of matrix B is 40. The detailed solution to find the determinant of matrix A is 5 and the determinant of matrix B is given below.
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Steps to find the determinant of matrix AB
When the determinant of matrix A is 5 and the determinant of matrix B is 40, the determinant of matrix AB can be found in the following ways:
- Let A and B are the square matrix of size ‘n’ then:
- determinant of (A).determinant of (B) = determinant of (A.B)
- We know that: the determinant of A is 5 and the determinant of B is 40
- determinant of (A.B) = determinant of (A).determinant of (B) = 5 × 40
- Therefore, determinant (AB) = 200
Summary:
The determinant of matrix A is 5 and the determinant of matrix B is 40. The determinant of matrix AB is?
When the determinant of the A matrix is 5 and the determinant of the B matrix is 40 then the determinant of the AB matrix will be 200. The step-by-step process to find the determinant of A and B has been illustrated above.
