Matrices and Determinants
Rank of a Matrix
Premium Question
Grade 12
Question:
The rank of the $n \times n$ identity matrix $I_n$ is:
(1) $n$
(2) $1$
(3) $n - 1$
(4) $0$
Step-by-Step Solution
Key Concept: Recall that the rank of a matrix equals the number of linearly independent rows (or columns) — examine the rows of the identity matrix and decide whether any one of them can be written as a combination of the others.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (1)