JEE Main & Advanced
Mathematics
Determinants & Matrices
Question Bank
Self Evaluation Test - Matrices
question_answer
Number of square sub-matrices of order 2 (sub-matrix is obtained by deleting appropriate number of rows and columns in a given matrix) that can be formed from the matrix \[\left[ \begin{matrix} 1 & 2 & -1 & 4 \\ 2 & 4 & 3 & 5 \\ -1 & -2 & 6 & -7 \\ \end{matrix} \right]\] is
A)12
B)15
C)18
D)\[{{2}^{12}}\]
Correct Answer:
C
Solution :
[c] The desired number of sub-matrices \[={{\,}^{4}}{{C}_{2}}\times {{\,}^{3}}{{C}_{2}}=18\]