GATE 2024 Engg. Mathematics Quiz 1

Which of the following is a scalar matrix?

Consider the following matrix A.

The value of x for which the matrix A is not invertible is?

A is a n × n matrix such that A² = I, and B is n×1 real vector, then AX=B has?

The value of a for which the following system has infinite solutions is: 
ax + y + 2z = 0 
x + 2y + z = 0 
2x + y + az = 0

Suppose A is a matrix of order 3 × 3 whose characteristics roots are 3, 2, –1. If B = A² – A,  then the determinant of |B| is __________ .