Question
Download Solution PDFIf A is the identity matrix of order 3 and B is its transpose, then what is the value of the determinant of the matrix C = A + B?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
1). Transpose of a Matrix:
The new matrix obtained by interchanging the rows and columns of the original matrix is called
the transpose of the matrix.
For example:
It is denoted by A' or AT.
2). For the addition and subtraction of two matrices, the order of matrices should be equal.
Calculation:
Given:
C = A + B
⇒
⇒
⇒ ∣C∣ = 2(4 - 0)
⇒ ∣C∣ = 8
∴ The determinant of matrix C is 8.
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