Let A be a matrix of order 2 $\times$ 2, whose entries are from the set {0, 1, 2, 3, 4, 5}. If the sum of all the entries of A is a prime number p, 2 < p < 8, then the number of such matrices A is ___________.

<p>$\because$ Sum of all entries of matrix A must be prime p such that 2 < p < 8 then sum of entries may be 3, 5 or 7.</p> <p>If sum is 3 then possible entries are (0, 0, 0, 3), (0, 0, 1, 2) or (0, 1, 1, 1).</p> <p>$\therefore$ Total number of matrices = 4 + 4 + 12 = 20</p> <p>If sum of 5 then possible entries are</p> <p>(0, 0, 0, 5), (0, 0, 1, 4), (0, 0, 2, 3), (0, 1, 1, 3), (0, 1, 2, 2) and (1, 1, 1, 2).</p> <p>$\therefore$ Total number of matrices = 4 + 12 + 12 + 12 + 12 + 4 = 56</p> <p>If sum is 7 then possible entries are</p> <p>(0, 0, 2, 5), (0, 0, 3, 4), (0, 1, 1, 5), (0, 3, 3, 1), (0, 2, 2, 3), (1, 1, 1, 4), (1, 2, 2, 2), (1, 1, 2, 3) and (0, 1, 2, 4).</p> <p>Total number of matrices with sum 7 = 104</p> <p>$\therefore$ Total number of required matrices</p> <p>= 20 + 56 + 104</p> <p>= 180</p>