Question:
If $P$ is a $3 \times 3$ real matrix such that $P^T=a P+(a-1) I$, where $a>$, then
If $P$ is a $3 \times 3$ real matrix such that $P^T=a P+(a-1) I$, where $a>$, then
Updated On: Nov 24, 2025
- $|\operatorname{Adj} P|>1$
- $|A d j P|=\frac{1}{2}$
- $P$ is a singular matrix
- $|A d j P|=1$
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The Correct Option is D
Solution and Explanation
So, the correct option is (D) : $|A d j P|=1$
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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.