Question:
If $A$ and $B$ are square matrices of order 3 such that $det A = 1$ and $ det B = -1$, then $det (- 10 AB) = ? $
If $A$ and $B$ are square matrices of order 3 such that $det A = 1$ and $ det B = -1$, then $det (- 10 AB) = ? $
Updated On: Jun 23, 2024
- 10
- -10
- -1000
- 1000
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The Correct Option is C
Solution and Explanation
$det (- 10 AB) = (- 10) det A$ and $B = (- 10) (1) (- 1) = 10 $
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Concepts Used:
Matrices
Matrix:
A matrix is a rectangular array of numbers, variables, symbols, or expressions that are defined for the operations like subtraction, addition, and multiplications. The size of a matrix is determined by the number of rows and columns in the matrix.
The basic operations that can be performed on matrices are:
- Addition of Matrices - The addition of matrices addition can only be possible if the number of rows and columns of both the matrices are the same.
- Subtraction of Matrices - Matrices subtraction is also possible only if the number of rows and columns of both the matrices are the same.
- Scalar Multiplication - The product of a matrix A with any number 'c' is obtained by multiplying every entry of the matrix A by c, is called scalar multiplication.
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- Transpose of Matrices - Interchanging of rows and columns is known as the transpose of matrices.