If A is sqaure matrix of order 3 such that |A|=3, them the value of |adj A| is ______
If A is sqaure matrix of order 3 such that |A|=3, them the value of |adj A| is ______
\((3)^2\)
\((3)^3\)
\((2)^3\)
\((2)^2\)
The Correct Option is A
Solution and Explanation
To find the value of \(|\text{adj } A|\) for a square matrix \(A\) of order 3 where \(|A|=3\), we use the formula for the determinant of the adjugate (adjoint) of a matrix:
\(|\text{adj } A| = |A|^{n-1}\)
where \(n\) is the order of the matrix. Here, \(n=3\).
Substituting the given value of \(|A|\):
\(|\text{adj } A| = 3^{3-1} = 3^2 = 9\)
Thus, the value of \(|\text{adj } A|\) is 9.
The correct option is (3)2.
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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.
- Multiplication of Matrices - Matrices multiplication is defined only if the number of columns in the first matrix and rows in the second matrix are equal.
- Transpose of Matrices - Interchanging of rows and columns is known as the transpose of matrices.